Research

37 pages, 7148 KiB

Open AccessArticle

Longitudinal Data Analysis Based on Bayesian Semiparametric Method

by Guimei Jiao, Jiajuan Liang, Fanjuan Wang, Xiaoli Chen, Shaokang Chen, Hao Li, Jing Jin, Jiali Cai and Fangjie Zhang

Axioms 2023, 12(5), 431; https://doi.org/10.3390/axioms12050431 - 27 Apr 2023

Cited by 1 | Viewed by 1033

Abstract

A Bayesian semiparametric model framework is proposed to analyze multivariate longitudinal data. The new framework leads to simple explicit posterior distributions of model parameters. It results in easy implementation of the MCMC algorithm for estimation of model parameters and demonstrates fast convergence. The [...] Read more.

A Bayesian semiparametric model framework is proposed to analyze multivariate longitudinal data. The new framework leads to simple explicit posterior distributions of model parameters. It results in easy implementation of the MCMC algorithm for estimation of model parameters and demonstrates fast convergence. The proposed model framework associated with the MCMC algorithm is validated by four covariance structures and a real-life dataset. A simple Monte Carlo study of the model under four covariance structures and an analysis of the real dataset show that the new model framework and its associated Bayesian posterior inferential method through the MCMC algorithm perform fairly well in the sense of easy implementation, fast convergence, and smaller root mean square errors compared with the same model without the specified autoregression structure. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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25 pages, 3838 KiB

Open AccessArticle

Mixture of Shanker Distributions: Estimation, Simulation and Application

by Tahani A. Abushal, Tabassum Naz Sindhu, Showkat Ahmad Lone, Marwa K. H. Hassan and Anum Shafiq

Axioms 2023, 12(3), 231; https://doi.org/10.3390/axioms12030231 - 22 Feb 2023

Cited by 2 | Viewed by 1065

Abstract

The Shanker distribution, a one-parameter lifetime distribution with an increasing hazard rate function, is recommended by Shanker for modelling lifespan data. In this study, we examine the theoretical and practical implications of 2-component mixture of Shanker model (2-CMSM). A significant feature of proposed [...] Read more.

The Shanker distribution, a one-parameter lifetime distribution with an increasing hazard rate function, is recommended by Shanker for modelling lifespan data. In this study, we examine the theoretical and practical implications of 2-component mixture of Shanker model (2-CMSM). A significant feature of proposed model’s hazard rate function is that it has rising, decreasing, and upside-down bathtub forms. We investigate the statistical characteristics of a mixed model, such as the probability-generating function, the factorial-moment-generating function, cumulants, the characteristic function, the Mills ratio, the mean residual life, and the mean time to failure. There is a graphic representation of density, mean, hazard rate functions, coefficient of variation, skewness, and kurtosis. Our final approach is to estimate the parameters of the mixture model using appropriate approaches such as maximum likelihood, least squares, and weighted least squares. Using a simulation analysis, we examined how the estimates behaved graphically. The simulation results demonstrated that, in the majority of cases, the maximum likelihood estimates have the smallest mean square errors among all other estimates. Finally, we observed that when the sample size rises, the precision measures decrease for all of the estimation techniques, indicating that all of the estimation approaches are consistent. Through two real data analyses, the suggested model’s validity and adaptability are contrasted with those of other models, including the mixture of the exponential distributions and the Lindley distributions . Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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19 pages, 424 KiB

Open AccessArticle

Partially Linear Additive Hazards Regression for Bivariate Interval-Censored Data

by Ximeng Zhang, Shishun Zhao, Tao Hu and Jianguo Sun

Axioms 2023, 12(2), 198; https://doi.org/10.3390/axioms12020198 - 13 Feb 2023

Viewed by 1136

Abstract

In this paper, we discuss regression analysis of bivariate interval-censored failure time data that often occur in biomedical and epidemiological studies. To solve this problem, we propose a kind of general and flexible copula-based semiparametric partly linear additive hazards models that can allow [...] Read more.

In this paper, we discuss regression analysis of bivariate interval-censored failure time data that often occur in biomedical and epidemiological studies. To solve this problem, we propose a kind of general and flexible copula-based semiparametric partly linear additive hazards models that can allow for both time-dependent covariates and possible nonlinear effects. For inference, a sieve maximum likelihood estimation approach based on Bernstein polynomials is proposed to estimate the baseline hazard functions and nonlinear covariate effects. The resulting estimators of regression parameters are shown to be consistent, asymptotically efficient and normal. A simulation study is conducted to assess the finite-sample performance of this method and the results show that it is effective in practice. Moreover, an illustration is provided. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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12 pages, 1071 KiB

Open AccessArticle

On the Estimation of the Binary Response Model

by Muhammad Amin, Muhammad Nauman Akram, B. M. Golam Kibria, Huda M. Alshanbari, Nahid Fatima and Ahmed Elhassanein

Axioms 2023, 12(2), 175; https://doi.org/10.3390/axioms12020175 - 08 Feb 2023

Viewed by 1229

Abstract

The binary logistic regression model (LRM) is practical in situations when the response variable (RV) is dichotomous. The maximum likelihood estimator (MLE) is generally considered to estimate the LRM parameters. However, in the presence of multicollinearity (MC), the MLE is not the correct [...] Read more.

The binary logistic regression model (LRM) is practical in situations when the response variable (RV) is dichotomous. The maximum likelihood estimator (MLE) is generally considered to estimate the LRM parameters. However, in the presence of multicollinearity (MC), the MLE is not the correct choice due to its inflated standard deviation (SD) and standard errors (SE) of the estimates. To combat MC, commonly used biased estimators, i.e., the Ridge estimators (RE) and Liu estimators (LEs), are preferred. However, most of the time, the traditional LE attains a negative value for its Liu parameter (LP), which is considered to be a major drawback. Therefore, to overcome this issue, we proposed a new adjusted LE for the binary LRM. Owing to numerical evaluation purposes, Monte Carlo simulation (MCS) study is performed under different conditions where bias and mean squared error are the performance criteria. Findings showed the superiority of our proposed estimator in comparison with the other estimation methods due to the existence of high but imperfect multicollinearity, which clearly means that it is consistent when the regressors are multicollinear. Furthermore, the findings demonstrated that whenever there is MC, the MLE is not the best choice. Finally, a real application is being considered to be evidence for the advantage of the intended estimator. The MCS and the application findings pointed out that the considered adjusted LE for the binary logistic regression model is a more efficient estimation method whenever the regressors are highly multicollinear. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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30 pages, 1386 KiB

Open AccessArticle

Statistical Inference of Truncated Cauchy Power-Inverted Topp–Leone Distribution under Hybrid Censored Scheme with Applications

by Rania A. H. Mohamed, Mohammed Elgarhy, Manal H. Alabdulhadi, Ehab M. Almetwally and Taha Radwan

Axioms 2023, 12(2), 148; https://doi.org/10.3390/axioms12020148 - 31 Jan 2023

Cited by 5 | Viewed by 1087

Abstract

In this article, a new two-parameter model called the truncated Cauchy power-inverted Topp–Leone (TCP-ITL) is constructed by merging the truncated Cauchy power -G (TCP-G) family with the inverted Topp–Leone (ITL) distribution. Some structural properties of the newly suggested model are obtained. Different types [...] Read more.

In this article, a new two-parameter model called the truncated Cauchy power-inverted Topp–Leone (TCP-ITL) is constructed by merging the truncated Cauchy power -G (TCP-G) family with the inverted Topp–Leone (ITL) distribution. Some structural properties of the newly suggested model are obtained. Different types of entropies are proposed under the TCP-ITL distribution. Under the complete and hybrid censored data, the maximum likelihood (ML), maximum product of spacing (MPSP), and Bayesian estimate approaches are explored. A simulation study is developed to test the proposed distribution’s restricted sample attributes. In the majority of cases, the numerical data revealed that the Bayesian estimates provided more accurate outcomes than the equivalent alternative estimates. The adaptability of the proposed approach is proven using examples from dependability, medicine, and engineering. A real-world data set is utilized to demonstrate the potential of the TCP-ITL distribution in comparison to other well-known distributions. The results of the model selection revealed that the proposed distribution is the best choice for the data sets under consideration. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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20 pages, 401 KiB

Open AccessArticle

A Method for Detecting Outliers from the Gamma Distribution

by Xiou Liao, Tongtong Wang and Guohua Zou

Axioms 2023, 12(2), 107; https://doi.org/10.3390/axioms12020107 - 19 Jan 2023

Cited by 1 | Viewed by 1614

Abstract

Outliers often occur during data collection, which could impact the result seriously and lead to a large inference error; therefore, it is important to detect outliers before data analysis. Gamma distribution is a popular distribution in statistics; this paper proposes a method for [...] Read more.

Outliers often occur during data collection, which could impact the result seriously and lead to a large inference error; therefore, it is important to detect outliers before data analysis. Gamma distribution is a popular distribution in statistics; this paper proposes a method for detecting multiple upper outliers from gamma (

m, θ

). For computing the critical value of the test statistic in our method, we derive the density function for the case of a single outlier and design two algorithms based on the Monte Carlo and the kernel density estimation for the case of multiple upper outliers. A simulation study shows that the test statistic proposed in this paper outperforms some common test statistics. Finally, we propose an improved testing method to reduce the impact of the swamping effect, which is demonstrated by real data analyses. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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13 pages, 295 KiB

Open AccessArticle

Direct Constructions of Uniform Designs under the Weighted Discrete Discrepancy

by Jiaqi Wang and Yu Tang

Axioms 2022, 11(12), 747; https://doi.org/10.3390/axioms11120747 - 19 Dec 2022

Viewed by 1145

Abstract

Uniform designs are widely used in many fields in view of their ability to reduce experimentalcosts. In a lot of practical cases, different factors may take different numbers of values, so a mixed-level uniform design is needed. Since it is not reasonable to [...] Read more.

Uniform designs are widely used in many fields in view of their ability to reduce experimentalcosts. In a lot of practical cases, different factors may take different numbers of values, so a mixed-level uniform design is needed. Since it is not reasonable to use the uniformity measure with the same weight for factors with different levels, the weighted discrete discrepancy was proposed in the existing literature. This paper discusses the construction method of mixed-level uniform designs under the weighted discrete discrepancy. The underlying method is to utilize some properties of partitioned difference families (PDFs) to obtain an infinite class of uniformly resolvable weighted balanced designs (URWBDs), which can directly produce corresponding uniform designs. Some examples are presented to illustrate the methods. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

27 pages, 699 KiB

Open AccessArticle

Statistical Inference of the Beta Binomial Exponential 2 Distribution with Application to Environmental Data

by Osama H. Mahmoud Hassan, Ibrahim Elbatal, Abdullah H. Al-Nefaie and Ahmed R. El-Saeed

Axioms 2022, 11(12), 740; https://doi.org/10.3390/axioms11120740 - 17 Dec 2022

Cited by 1 | Viewed by 1097

Abstract

A new four-parameter lifetime distribution called the beta binomial exponential 2

(B B E 2)

distribution is proposed. Some mathematical features, including quantile function, moments, generating function and characteristic function, of the

B B E 2

distribution, are computed. When the [...] Read more.

A new four-parameter lifetime distribution called the beta binomial exponential 2

(B B E 2)

distribution is proposed. Some mathematical features, including quantile function, moments, generating function and characteristic function, of the

B B E 2

distribution, are computed. When the life test is truncated at a predetermined time, acceptance sampling plans (ASP) are constructed for the

B B E 2

distribution. The truncation time is supposed to represent the median lifetime of the

B B E 2

distribution with predetermined factors for the smallest sample size required to guarantee that the prescribed life test is achieved at a given consumer’s risk. Some numerical results for a given consumer’s risk,

B B E 2

distribution parameters and truncation time are derived. Classical (maximum likelihood and maximum product of spacing estimation methods) and Bayesian estimation approaches are utilized to estimate the model parameters. The performance of the model parameters is examined through the simulation study by using the three different approaches of estimation. Subsequently, we examine real-world data applications to demonstrate the versatility and potential of the

B B E 2

model. A real-world application demonstrates that the new distribution can offer a better fit than other competitive lifetime models. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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18 pages, 1647 KiB

Open AccessArticle

Discrete Single-Factor Extension of the Exponential Distribution: Features and Modeling

by Mahmoud El-Morshedy, Hend S. Shahen, Bader Almohaimeed and Mohamed S. Eliwa

Axioms 2022, 11(12), 737; https://doi.org/10.3390/axioms11120737 - 16 Dec 2022

Viewed by 985

Abstract

The importance of counting data modeling and its applications to real-world phenomena has been highlighted in several research studies. The present study focuses on a one-parameter discrete distribution that can be derived via the survival discretization approach. The proposed model has explicit forms [...] Read more.

The importance of counting data modeling and its applications to real-world phenomena has been highlighted in several research studies. The present study focuses on a one-parameter discrete distribution that can be derived via the survival discretization approach. The proposed model has explicit forms for its statistical properties. It can be applied to discuss asymmetric “right skewed” data with long “heavy” tails. Its failure rate function can be used to discuss the phenomena with a monotonically decreasing or unimodal failure rate shape. Further, it can be utilized as a probability tool to model and discuss over- and under-dispersed data. Various estimation techniques are reported and discussed in detail. A simulation study is performed to test the property of the estimator. Finally, three real data sets are analyzed to prove the notability of the introduced model. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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12 pages, 315 KiB

Open AccessArticle

Projection Uniformity of Asymmetric Fractional Factorials

by Kang Wang, Zujun Ou, Hong Qin and Na Zou

Axioms 2022, 11(12), 716; https://doi.org/10.3390/axioms11120716 - 10 Dec 2022

Cited by 1 | Viewed by 1527

Abstract

The objective of this paper is to study the issue of the projection uniformity of asymmetric fractional factorials. On the basis of level permutation and mixture discrepancy, the average projection mixture discrepancy to measure the uniformity for low-dimensional projection designs is defined, the [...] Read more.

The objective of this paper is to study the issue of the projection uniformity of asymmetric fractional factorials. On the basis of level permutation and mixture discrepancy, the average projection mixture discrepancy to measure the uniformity for low-dimensional projection designs is defined, the uniformity pattern and minimum projection uniformity criterion are presented for evaluating and comparing any asymmetric factorials. Moreover, lower bounds to uniformity pattern have been obtained, and some illustrative examples are also provided. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

19 pages, 1329 KiB

Open AccessArticle

Representative Points Based on Power Exponential Kernel Discrepancy

by Zikang Xiong, Yao Xiao, Jianhui Ning and Hong Qin

Axioms 2022, 11(12), 711; https://doi.org/10.3390/axioms11120711 - 09 Dec 2022

Viewed by 1272

Abstract

Representative points (rep-points) are a set of points that are optimally chosen for representing a big original data set or a target distribution in terms of a statistical criterion, such as mean square error and discrepancy. Most of the existing criteria can only [...] Read more.

Representative points (rep-points) are a set of points that are optimally chosen for representing a big original data set or a target distribution in terms of a statistical criterion, such as mean square error and discrepancy. Most of the existing criteria can only assure the representing properties in the whole variable space. In this paper, a new kernel discrepancy, named power exponential kernel discrepancy (PEKD), is proposed to measure the representativeness of the point set with respect to the general multivariate distribution. Different from the commonly used criteria, PEKD can improve the projection properties of the point set, which is important in high-dimensional circumstances. Some theoretical results are presented for understanding the new discrepancy better and guiding the hyperparameter setting. An efficient algorithm for searching rep-points under the PEKD criterion is presented and its convergence has also been proven. Examples are given to illustrate its potential applications in the numerical integration, uncertainty propagation, and reduction of Markov Chain Monte Carlo chains. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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18 pages, 469 KiB

Open AccessArticle

A Unified Test for the AR Error Structure of an Autoregressive Model

by Xinyi Wei, Xiaohui Liu, Yawen Fan, Li Tan and Qing Liu

Axioms 2022, 11(12), 690; https://doi.org/10.3390/axioms11120690 - 01 Dec 2022

Viewed by 1220

Abstract

A direct application of autoregressive (AR) models with independent and identically distributed (iid) errors is sometimes inadequate to fit the time series data well. A natural alternative is further to assume the model errors following an AR process, whose structure however has essential [...] Read more.

A direct application of autoregressive (AR) models with independent and identically distributed (iid) errors is sometimes inadequate to fit the time series data well. A natural alternative is further to assume the model errors following an AR process, whose structure however has essential impacts on the statistical inferences related to the autoregressive models. In this paper, we construct a new unified test for checking the AR error structure based on the empirical likelihood method. The proposed test is desirable because its limit distribution is always chi-squared regardless of whether the autoregressive model is stationary or non-stationary, with or without an intercept term. Some simulations are also provided to illustrate the finite sample performance of this test. Finally, we apply the proposed test to a financial real data set. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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19 pages, 675 KiB

Open AccessArticle

Confidence Intervals for the Ratio of Variances of Delta-Gamma Distributions with Applications

by Wansiri Khooriphan, Sa-Aat Niwitpong and Suparat Niwitpong

Axioms 2022, 11(12), 689; https://doi.org/10.3390/axioms11120689 - 30 Nov 2022

Cited by 3 | Viewed by 1077

Abstract

Since rainfall data often contain zero observations, the ratio of the variances of delta-gamma distributions can be used to compare the rainfall dispersion between two rainfall datasets. To this end, we constructed the confidence interval for the ratio of the variances of two [...] Read more.

Since rainfall data often contain zero observations, the ratio of the variances of delta-gamma distributions can be used to compare the rainfall dispersion between two rainfall datasets. To this end, we constructed the confidence interval for the ratio of the variances of two delta-gamma distributions by using the fiducial quantity method, Bayesian credible intervals based on the Jeffreys, uniform, or normal-gamma-beta priors, and highest posterior density (HPD) intervals based on the Jeffreys, uniform, or normal-gamma-beta priors. The performances of the proposed confidence interval methods were evaluated in terms of their coverage probabilities and average lengths via Monte Carlo simulation. Our findings show that the HPD intervals based on Jeffreys prior and the normal-gamma-beta prior are both suitable for datasets with a small and large probability of containing zeros, respectively. Rainfall data from Phrae province, Thailand, are used to illustrate the practicability of the proposed methods with real data. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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18 pages, 723 KiB

Open AccessArticle

A Unit Half-Logistic Geometric Distribution and Its Application in Insurance

by Ahmed T. Ramadan, Ahlam H. Tolba and Beih S. El-Desouky

Axioms 2022, 11(12), 676; https://doi.org/10.3390/axioms11120676 - 28 Nov 2022

Cited by 9 | Viewed by 1416

Abstract

A new one parameter distribution recently was proposed for modelling lifetime data called half logistic-geometric (HLG) distribution. In this paper, appropriate transformation is considered for HLG distribution and a new distribution is derived called unit half logistic-geometric (UHLG) distribution for modelling bounded data [...] Read more.

A new one parameter distribution recently was proposed for modelling lifetime data called half logistic-geometric (HLG) distribution. In this paper, appropriate transformation is considered for HLG distribution and a new distribution is derived called unit half logistic-geometric (UHLG) distribution for modelling bounded data in the interval (0, 1). Some important statistical properties are investigated with a closed form quantile function. Some methods of parameter estimation are introduced to evaluate the distribution parameter and a simulation study is introduced to compare these different methods. A real data application in the insurance field is introduced to show the flexibility of the new distribution modelling such data comparing with other distributions. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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27 pages, 2059 KiB

Open AccessArticle

New Robust Estimators for Handling Multicollinearity and Outliers in the Poisson Model: Methods, Simulation and Applications

by Issam Dawoud, Fuad A. Awwad, Elsayed Tag Eldin and Mohamed R. Abonazel

Axioms 2022, 11(11), 612; https://doi.org/10.3390/axioms11110612 - 03 Nov 2022

Cited by 5 | Viewed by 1839

Abstract

The Poisson maximum likelihood (PML) is used to estimate the coefficients of the Poisson regression model (PRM). Since the resulting estimators are sensitive to outliers, different studies have provided robust Poisson regression estimators to alleviate this problem. Additionally, the PML estimator is sensitive [...] Read more.

The Poisson maximum likelihood (PML) is used to estimate the coefficients of the Poisson regression model (PRM). Since the resulting estimators are sensitive to outliers, different studies have provided robust Poisson regression estimators to alleviate this problem. Additionally, the PML estimator is sensitive to multicollinearity. Therefore, several biased Poisson estimators have been provided to cope with this problem, such as the Poisson ridge estimator, Poisson Liu estimator, Poisson Kibria–Lukman estimator, and Poisson modified Kibria–Lukman estimator. Despite different Poisson biased regression estimators being proposed, there has been no analysis of the robust version of these estimators to deal with the two above-mentioned problems simultaneously, except for the robust Poisson ridge regression estimator, which we have extended by proposing three new robust Poisson one-parameter regression estimators, namely, the robust Poisson Liu (RPL), the robust Poisson Kibria–Lukman (RPKL), and the robust Poisson modified Kibria–Lukman (RPMKL). Theoretical comparisons and Monte Carlo simulations were conducted to show the proposed performance compared with the other estimators. The simulation results indicated that the proposed RPL, RPKL, and RPMKL estimators outperformed the other estimators in different scenarios, in cases where both problems existed. Finally, we analyzed two real datasets to confirm the results. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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34 pages, 5402 KiB

Open AccessArticle

Amoud Class for Hazard-Based and Odds-Based Regression Models: Application to Oncology Studies

by Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa, Christophe Chesneau, Huda M. Alshanbari and Abdal-Aziz H. El-Bagoury

Axioms 2022, 11(11), 606; https://doi.org/10.3390/axioms11110606 - 01 Nov 2022

Cited by 5 | Viewed by 3604

Abstract

The purpose of this study is to propose a novel, general, tractable, fully parametric class for hazard-based and odds-based models of survival regression for the analysis of censored lifetime data, named as the “Amoud class (AM)” of models. This generality was attained using [...] Read more.

The purpose of this study is to propose a novel, general, tractable, fully parametric class for hazard-based and odds-based models of survival regression for the analysis of censored lifetime data, named as the “Amoud class (AM)” of models. This generality was attained using a structure resembling the general class of hazard-based regression models, with the addition that the baseline odds function is multiplied by a link function. The class is broad enough to cover a number of widely used models, including the proportional hazard model, the general hazard model, the proportional odds model, the general odds model, the accelerated hazards model, the accelerated odds model, and the accelerated failure time model, as well as combinations of these. The proposed class incorporates the analysis of crossing survival curves. Based on a versatile parametric distribution (generalized log-logistic) for the baseline hazard, we introduced a technique for applying these various hazard-based and odds-based regression models. This distribution allows us to cover the most common hazard rate shapes in practice (decreasing, constant, increasing, unimodal, and reversible unimodal), and various common survival distributions (Weibull, Burr-XII, log-logistic, exponential) are its special cases. The proposed model has good inferential features, and it performs well when different information criteria and likelihood ratio tests are used to select hazard-based and odds-based regression models. The proposed model’s utility is demonstrated by an application to a right-censored lifetime dataset with crossing survival curves. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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13 pages, 399 KiB

Open AccessArticle

Enhanced Lot Acceptance Testing Based on Defect Counts and Posterior Odds Ratios

by Arturo J. Fernández

Axioms 2022, 11(11), 604; https://doi.org/10.3390/axioms11110604 - 29 Oct 2022

Viewed by 1041

Abstract

Optimal defects-per-unit test plans based on posterior odds ratios are developed for the disposition of product lots. The number of nonconformities per unit is modeled by the Conway–Maxwell–Poisson distribution rather than the typical Poisson model. In essence, a submitted batch is conforming if [...] Read more.

Optimal defects-per-unit test plans based on posterior odds ratios are developed for the disposition of product lots. The number of nonconformities per unit is modeled by the Conway–Maxwell–Poisson distribution rather than the typical Poisson model. In essence, a submitted batch is conforming if its posterior acceptability is sufficiently large. First, a useful approximation of the optimal test plan is derived in closed form using the asymptotic normality of the log ratio. A mixed-integer nonlinear programming problem is then solved via Monte Carlo simulation to find the smallest number of inspected items per lot and the maximum tolerable posterior odds ratio. The methodology is applied to the manufacturing of paper and glass. The suggested sampling plan for lot sentencing provides the specified protections to both manufacturers and customers and minimizes the needed sample size. In terms of inspection effort and accuracy, the proposed approach is virtually an advantageous extension of the classical frequentist perspective. In many practical cases, it yields more precise assessments of the current consumer and producer risks, as well as more realistic decision rules. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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20 pages, 1649 KiB

Open AccessArticle

Testing Multivariate Normality Based on t-Representative Points

by Jiajuan Liang, Ping He and Jun Yang

Axioms 2022, 11(11), 587; https://doi.org/10.3390/axioms11110587 - 24 Oct 2022

Cited by 2 | Viewed by 1320

Abstract

Testing multivariate normality is an ever-lasting interest in the goodness-of-fit area since the classical Pearson’s chi-squared test. Among the numerous approaches in the construction of tests for multivariate normality, normal characterization is one of the common approaches, which can be divided into the [...] Read more.

Testing multivariate normality is an ever-lasting interest in the goodness-of-fit area since the classical Pearson’s chi-squared test. Among the numerous approaches in the construction of tests for multivariate normality, normal characterization is one of the common approaches, which can be divided into the necessary and sufficient characterization and necessary-only characterization. We construct a test for multivariate normality by combining the necessary-only characterization and the idea of statistical representative points in this paper. The main idea is to transform a high-dimensional sample into a one-dimensional one through the necessary normal characterization and then employ the representative-point-based Pearson’s chi-squared test. A limited Monte Carlo study shows a considerable power improvement of the representative-point-based chi-square test over the traditional one. An illustrative example is given to show the supplemental function of the new test when used together with existing ones in the literature. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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22 pages, 1472 KiB

Open AccessArticle

Statistical Analysis of Alpha Power Exponential Parameters Using Progressive First-Failure Censoring with Applications

by Mazen Nassar, Refah Alotaibi and Ahmed Elshahhat

Axioms 2022, 11(10), 553; https://doi.org/10.3390/axioms11100553 - 13 Oct 2022

Cited by 1 | Viewed by 1311

Abstract

This paper is an endeavor to investigate some estimation problems of the unknown parameters and some reliability measures of the alpha power exponential distribution in the presence of progressive first-failure censored data. In this regard, the classical and Bayesian approaches are considered to [...] Read more.

This paper is an endeavor to investigate some estimation problems of the unknown parameters and some reliability measures of the alpha power exponential distribution in the presence of progressive first-failure censored data. In this regard, the classical and Bayesian approaches are considered to acquire the point and interval estimates of the different quantities. The maximum likelihood approach is proposed to obtain the estimates of the unknown parameters, reliability, and hazard rate functions. The approximate confidence intervals are also considered. The Bayes estimates are obtained by considering both symmetric and asymmetric loss functions. The Bayes estimates and the associated highest posterior density credible intervals are given by applying the Monte Carlo Markov Chain technique. Due to the complexity of the given estimators which cannot be compared theoretically, a simulation study is implemented to compare the performance of the different procedures. In addition, diverse optimality criteria are employed to pick the best progressive censoring plans. Two engineering applications are considered to illustrate the applicability of the offered estimators. The numerical outcomes showed that the Bayes estimates based on symmetric or asymmetric loss functions perform better than other estimates in terms of minimum root mean square errors and interval lengths. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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16 pages, 3731 KiB

Open AccessArticle

A New 3-Parameter Bounded Beta Distribution: Properties, Estimation, and Applications

by Faiza A. Althubyani, Ahmed M. T. Abd El-Bar, Mohamad A. Fawzy and Ahmed M. Gemeay

Axioms 2022, 11(10), 504; https://doi.org/10.3390/axioms11100504 - 26 Sep 2022

Cited by 7 | Viewed by 1662

Abstract

This study presents a new three-parameter beta distribution defined on the unit interval, which can have increasing, decreasing, left-skewed, right-skewed, approximately symmetric, bathtub, and upside-down bathtub shaped densities, and increasing, U, and bathtub shaped hazard rates. This model can define well-known distributions with [...] Read more.

This study presents a new three-parameter beta distribution defined on the unit interval, which can have increasing, decreasing, left-skewed, right-skewed, approximately symmetric, bathtub, and upside-down bathtub shaped densities, and increasing, U, and bathtub shaped hazard rates. This model can define well-known distributions with various parameters and supports, such as Kumaraswamy, beta exponential, exponential, exponentiated exponential, uniform, the generalized beta of the first kind, and beta power distributions. We present a comprehensive account of the mathematical features of the new model. Maximum likelihood methods and a Bayesian method under squared error and linear exponential loss functions are presented; also, approximate confidence intervals are obtained. We present a simulation study to compare all the results. Two real-world data sets are analyzed to demonstrate the utility and adaptability of the proposed model. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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19 pages, 404 KiB

Open AccessArticle

Statistical Inference for Odds Ratio of Two Proportions in Bilateral Correlated Data

by Zhiming Li and Changxing Ma

Axioms 2022, 11(10), 502; https://doi.org/10.3390/axioms11100502 - 25 Sep 2022

Viewed by 1304

Abstract

Bilateral correlated data frequently arise in medical clinical studies such as otolaryngology and ophthalmology. Based on an equal correlation coefficient model, this paper mainly aimed to investigate the statistical inference for the odds ratio of two proportions in bilateral correlated data, including not [...] Read more.

Bilateral correlated data frequently arise in medical clinical studies such as otolaryngology and ophthalmology. Based on an equal correlation coefficient model, this paper mainly aimed to investigate the statistical inference for the odds ratio of two proportions in bilateral correlated data, including not only three test procedures but also four confidence interval (CI) constructions. Through iterative algorithms, all unknown parameters are estimated in order to construct the likelihood ratio, score and Wald-type tests. Furthermore, the profile likelihood CI, score CI, and Wald-type CI are obtained by the bisection root-finding algorithm. We provided another Wald-type CI based on an asymptotic normality property. The performance of the proposed tests were investigated with regard to empirical type I error rate and power, and CI methods were compared in terms of mean coverage probability and mean interval width. Numerical simulations show that the score test is more robust, and has higher power than other tests. The score CI also has a shorter interval width, and its coverage probability is closer to 0.95. A real example is used to illustrate the proposed methods. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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27 pages, 1890 KiB

Open AccessArticle

Inferences of a Mixture Bivariate Alpha Power Exponential Model with Engineering Application

by Refah Alotaibi, Mazen Nassar, Indranil Ghosh, Hoda Rezk and Ahmed Elshahhat

Axioms 2022, 11(9), 459; https://doi.org/10.3390/axioms11090459 - 07 Sep 2022

Cited by 4 | Viewed by 1315

Abstract

The univariate alpha power exponential (APE) distribution has several appealing characteristics. It behaves similarly to Weibull, Gamma, and generalized exponential distributions with two parameters. In this paper, we consider different bivariate mixture models starting with two independent univariate APE models, and, in the [...] Read more.

The univariate alpha power exponential (APE) distribution has several appealing characteristics. It behaves similarly to Weibull, Gamma, and generalized exponential distributions with two parameters. In this paper, we consider different bivariate mixture models starting with two independent univariate APE models, and, in the latter case, starting from two dependent APE models. Several useful structural properties of such a mixture model (under the assumption of two independent APE distribution) are discussed. Bivariate APE (BAPE), in short, modelled under the dependent set up are also discussed in the context of a copula-based construction. Inferential aspects under the classical and under the Bayesian paradigm are considered to estimate the model parameters, and a simulation study is conducted for this purpose. For illustrative purposes, a well-known motor data is re-analyzed to exhibit the flexibility of the proposed bivariate mixture model. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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23 pages, 4666 KiB

Open AccessArticle

Bayesian and Non-Bayesian Analysis of Exponentiated Exponential Stress–Strength Model Based on Generalized Progressive Hybrid Censoring Process

by Manal M. Yousef, Amal S. Hassan, Huda M. Alshanbari, Abdal-Aziz H. El-Bagoury and Ehab M. Almetwally

Axioms 2022, 11(9), 455; https://doi.org/10.3390/axioms11090455 - 05 Sep 2022

Cited by 11 | Viewed by 1524

Abstract

In many real-life scenarios, systems frequently perform badly in difficult operating situations. The multiple failures that take place when systems reach their lower, higher, or extreme functioning states typically receive little attention from researchers. This study uses generalized progressive hybrid censoring to discuss [...] Read more.

In many real-life scenarios, systems frequently perform badly in difficult operating situations. The multiple failures that take place when systems reach their lower, higher, or extreme functioning states typically receive little attention from researchers. This study uses generalized progressive hybrid censoring to discuss the inference of

R = P (X < Y < Z)

for a component when it is exposed to two stresses,

Y, Z

, and it has one strength X that is regarded. We assume that both the stresses and strength variables follow an exponentiated exponential distribution with a common scale parameter. We obtain R’s maximum likelihood estimator and approximate confidence intervals. In addition, the Bayesian estimators for symmetric, such as squared error, and asymmetric loss functions, such as linear exponential, are developed. Credible intervals with the highest posterior densities are established. Monte Carlo simulations are used to evaluate and compare the effectiveness of the many proposed estimators. The process is then precisely described using an analysis of real data. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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19 pages, 897 KiB

Open AccessArticle

Inference of Reliability Analysis for Type II Half Logistic Weibull Distribution with Application of Bladder Cancer

by Rania A. H. Mohamed, Ahlam H. Tolba, Ehab M. Almetwally and Dina A. Ramadan

Axioms 2022, 11(8), 386; https://doi.org/10.3390/axioms11080386 - 06 Aug 2022

Cited by 9 | Viewed by 1301

Abstract

The estimation of the unknown parameters of Type II Half Logistic Weibull (TIIHLW) distribution was analyzed in this paper. The maximum likelihood and Bayes methods are used as estimation methods. These estimators are used to estimate the fuzzy reliability function and to choose [...] Read more.

The estimation of the unknown parameters of Type II Half Logistic Weibull (TIIHLW) distribution was analyzed in this paper. The maximum likelihood and Bayes methods are used as estimation methods. These estimators are used to estimate the fuzzy reliability function and to choose the best estimator of the fuzzy reliability function by comparing the mean square error (MSE). The simulation’s results showed that fuzziness is better than reality for all sample sizes, and fuzzy reliability at Bayes predicted estimates is better than the maximum likelihood technique. It produces the lowest average MSE until a sample size of n = 50 is obtained. A simulated data set is applied to diagnose the performance of the two techniques applied here. A real data set is used as a practice for the model discussed and developed the maximum likelihood estimate alternative model of TIIHLW as Topp Leone inverted Kumaraswamy, modified Kies inverted Topp–Leone, Kumaraswamy Weibull–Weibull, Marshall–Olkin alpha power inverse Weibull, and odd Weibull inverted Topp–Leone. We conclude that the TIIHLW is the best distribution fit for this data. Full article

(This article belongs to the Special Issue Computational Statistics & Data Analysis)

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