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Stats, Volume 2, Issue 1 (March 2019) – 12 articles

Cover Story (view full-size image): Published results are rich sources of information. However, although the information is readily available, the format is often inconvenient. Instead of mean and standard deviation, articles may report the median, interquartile or range. Extracting the mean and standard deviation from these summary statistics has a long and rich tradition. Despite this fact, the formulas routinely used for extraction do not take into account the uncertainty of the resulting estimates. Assessment of the uncertainty of these estimates requires a probabilistic approach. This paper assesses the possibility of extraction of means and their associated confidence intervals when only the range is made available. The article uses maximum likelihood estimation with order statistics (MLEOS). The feasibility of likelihood based confidence intervals are demonstrated via simulations and two real life examples. View this paper.
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10 pages, 758 KiB  
Article
Confidence Intervals for the Signal-to-Noise Ratio and Difference of Signal-to-Noise Ratios of Log-Normal Distributions
by Warisa Thangjai and Sa-Aat Niwitpong
Stats 2019, 2(1), 164-173; https://doi.org/10.3390/stats2010012 - 27 Feb 2019
Cited by 9 | Viewed by 3759
Abstract
In this article, we propose approaches for constructing confidence intervals for the single signal-to-noise ratio (SNR) of a log-normal distribution and the difference in the SNRs of two log-normal distributions. The performances of all of the approaches were compared, in terms of the [...] Read more.
In this article, we propose approaches for constructing confidence intervals for the single signal-to-noise ratio (SNR) of a log-normal distribution and the difference in the SNRs of two log-normal distributions. The performances of all of the approaches were compared, in terms of the coverage probability and average length, using Monte Carlo simulations for varying values of the SNRs and sample sizes. The simulation studies demonstrate that the generalized confidence interval (GCI) approach performed well, in terms of coverage probability and average length. As a result, the GCI approach is recommended for the confidence interval estimation for the SNR and the difference in SNRs of two log-normal distributions. Full article
16 pages, 398 KiB  
Article
A New Inference Approach for Type-II Generalized Birnbaum-Saunders Distribution
by Naijun Sha
Stats 2019, 2(1), 148-163; https://doi.org/10.3390/stats2010011 - 19 Feb 2019
Viewed by 1514
Abstract
The Birnbaum-Saunders (BS) distribution, with its generalizations, has been successfully applied in a wide variety of fields. One generalization, type-II generalized BS (denoted as GBS-II), has been developed and attracted considerable attention in recent years. In this article, we propose a new simple [...] Read more.
The Birnbaum-Saunders (BS) distribution, with its generalizations, has been successfully applied in a wide variety of fields. One generalization, type-II generalized BS (denoted as GBS-II), has been developed and attracted considerable attention in recent years. In this article, we propose a new simple and convenient procedure of inference approach for GBS-II distribution. An extensive simulation study is carried out to assess performance of the methods under various settings of parameter values with different sample sizes. Real data are analyzed for illustrative purposes to display the efficiency of the proposed method. Full article
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27 pages, 493 KiB  
Article
Saddlepoint Approximation for Data in Simplices: A Review with New Applications
by Riccardo Gatto
Stats 2019, 2(1), 121-147; https://doi.org/10.3390/stats2010010 - 18 Feb 2019
Viewed by 2075
Abstract
This article provides a review of the saddlepoint approximation for a M-statistic of a sample of nonnegative random variables with fixed sum. The sample vector follows the multinomial, the multivariate hypergeometric, the multivariate Polya or the Dirichlet distributions. The main objective is to [...] Read more.
This article provides a review of the saddlepoint approximation for a M-statistic of a sample of nonnegative random variables with fixed sum. The sample vector follows the multinomial, the multivariate hypergeometric, the multivariate Polya or the Dirichlet distributions. The main objective is to provide a complete presentation in terms of a single and unambiguous notation of the common mathematical framework of these four situations: the simplex sample space and the underlying general urn model. Some important applications are reviewed and special attention is given to recent applications to models of circular data. Some novel applications are developed and studied numerically. Full article
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10 pages, 666 KiB  
Article
Bayesian Inference for the Difference of Two Proportion Parameters in Over-Reported Two-Sample Binomial Data Using the Doubly Sample
by Dewi Rahardja
Stats 2019, 2(1), 111-120; https://doi.org/10.3390/stats2010009 - 11 Feb 2019
Cited by 2 | Viewed by 2639
Abstract
We construct a point and interval estimation using a Bayesian approach for the difference of two population proportion parameters based on two independent samples of binomial data subject to one type of misclassification. Specifically, we derive an easy-to-implement closed-form algorithm for drawing from [...] Read more.
We construct a point and interval estimation using a Bayesian approach for the difference of two population proportion parameters based on two independent samples of binomial data subject to one type of misclassification. Specifically, we derive an easy-to-implement closed-form algorithm for drawing from the posterior distributions. For illustration, we applied our algorithm to a real data example. Finally, we conduct simulation studies to demonstrate the efficiency of our algorithm for Bayesian inference. Full article
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7 pages, 737 KiB  
Article
Likelihood Confidence Intervals When Only Ranges Are Available
by Szilárd Nemes
Stats 2019, 2(1), 104-110; https://doi.org/10.3390/stats2010008 - 06 Feb 2019
Cited by 3 | Viewed by 1978
Abstract
Research papers represent an important and rich source of comparative data. The change is to extract the information of interest. Herein, we look at the possibilities to construct confidence intervals for sample averages when only ranges are available with maximum likelihood estimation with [...] Read more.
Research papers represent an important and rich source of comparative data. The change is to extract the information of interest. Herein, we look at the possibilities to construct confidence intervals for sample averages when only ranges are available with maximum likelihood estimation with order statistics (MLEOS). Using Monte Carlo simulation, we looked at the confidence interval coverage characteristics for likelihood ratio and Wald-type approximate 95% confidence intervals. We saw indication that the likelihood ratio interval had better coverage and narrower intervals. For single parameter distributions, MLEOS is directly applicable. For location-scale distribution is recommended that the variance (or combination of it) to be estimated using standard formulas and used as a plug-in. Full article
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15 pages, 553 KiB  
Article
A Support Vector Machine Based Approach for Predicting the Risk of Freshwater Disease Emergence in England
by Hossein Hassani, Emmanuel S. Silva, Marine Combe, Demetra Andreou, Mansi Ghodsi, Mohammad Reza Yeganegi and Rodolphe E. Gozlan
Stats 2019, 2(1), 89-103; https://doi.org/10.3390/stats2010007 - 05 Feb 2019
Cited by 6 | Viewed by 2715
Abstract
Disease emergence, in the last decades, has had increasingly disproportionate impacts on aquatic freshwater biodiversity. Here, we developed a new model based on Support Vector Machines (SVM) for predicting the risk of freshwater fish disease emergence in England. Following a rigorous training process [...] Read more.
Disease emergence, in the last decades, has had increasingly disproportionate impacts on aquatic freshwater biodiversity. Here, we developed a new model based on Support Vector Machines (SVM) for predicting the risk of freshwater fish disease emergence in England. Following a rigorous training process and simulations, the proposed SVM model was validated and reported high accuracy rates for predicting the risk of freshwater fish disease emergence in England. Our findings suggest that the disease monitoring strategy employed in England could be successful at preventing disease emergence in certain parts of England, as areas in which there were high fish introductions were not correlated with high disease emergence (which was to be expected from the literature). We further tested our model’s predictions with actual disease emergence data using Chi-Square tests and test of Mutual Information. The results identified areas that require further attention and resource allocation to curb future freshwater disease emergence successfully. Full article
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19 pages, 841 KiB  
Article
Testing for Equality of Parameters from Different Load-Sharing Systems
by Stefan Bedbur and Udo Kamps
Stats 2019, 2(1), 70-88; https://doi.org/10.3390/stats2010006 - 29 Jan 2019
Cited by 2 | Viewed by 1555
Abstract
In reliability, sequential order statistics serve as a model for the component lifetimes of k-out-of-n systems, which are operating as long as k out of n components are operating. In contrast to modelling with order statistics, load-sharing effects and other impacts [...] Read more.
In reliability, sequential order statistics serve as a model for the component lifetimes of k-out-of-n systems, which are operating as long as k out of n components are operating. In contrast to modelling with order statistics, load-sharing effects and other impacts of failures on the performance of the remaining components may be taken into consideration. Inference for associated load-sharing parameters, as well as for the underlying baseline distribution, is then of particular interest. In a setup of multiple samples of sequential order statistics modelling the component lifetimes of possibly differently structured k-out-of-n systems, we provide exact statistical tests to check for common load-sharing or common baseline-distribution parameters. In the two-sample case, critical values for the corresponding test statistics are tabulated for small sample sizes, and the asymptotic distributions of the test statistics under the null hypotheses are derived. Based on a simulation study, power comparisons are addressed. The proposed tests may be applied to detect significant differences between systems or to decide whether a meta-analysis of the data may be conducted to increase the performance of subsequent inferential procedures. Full article
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15 pages, 2720 KiB  
Article
Tracking Poisson Parameter for Non-Stationary Discontinuous Time Series with Taylor’s Abnormal Fluctuation Scaling
by Gen Sakoda, Hideki Takayasu and Misako Takayasu
Stats 2019, 2(1), 55-69; https://doi.org/10.3390/stats2010005 - 23 Jan 2019
Cited by 2 | Viewed by 2357
Abstract
We propose a parameter estimation method for non-stationary Poisson time series with the abnormal fluctuation scaling, known as Taylor’s law. By introducing the effect of Taylor’s fluctuation scaling into the State Space Model with the Particle Filter, the underlying Poisson parameter’s time evolution [...] Read more.
We propose a parameter estimation method for non-stationary Poisson time series with the abnormal fluctuation scaling, known as Taylor’s law. By introducing the effect of Taylor’s fluctuation scaling into the State Space Model with the Particle Filter, the underlying Poisson parameter’s time evolution is estimated correctly from given non-stationary time series data with abnormally large fluctuations. We also developed a discontinuity detection method which enables tracking the Poisson parameter even for time series including sudden discontinuous jumps. As an example of application of this new general method, we analyzed Point-of-Sales data in convenience stores to estimate change of probability of purchase of commodities under fluctuating number of potential customers. The effectiveness of our method for Poisson time series with non-stationarity, large discontinuities and Taylor’s fluctuation scaling is verified by artificial and actual time series. Full article
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21 pages, 1251 KiB  
Article
One-Parameter Weibull-Type Distribution, Its Relative Entropy with Respect to Weibull and a Fractional Two-Parameter Exponential Distribution
by Aris Alexopoulos
Stats 2019, 2(1), 34-54; https://doi.org/10.3390/stats2010004 - 21 Jan 2019
Cited by 4 | Viewed by 7936
Abstract
A new one-parameter distribution is presented with similar mathematical characteristics to the two parameter conventional Weibull. It has an estimator that only depends on the sample mean. The relative entropy with respect to the Weibull distribution is derived in order to examine the [...] Read more.
A new one-parameter distribution is presented with similar mathematical characteristics to the two parameter conventional Weibull. It has an estimator that only depends on the sample mean. The relative entropy with respect to the Weibull distribution is derived in order to examine the level of similarity between them. The performance of the new distribution is compared to the Weibull and in some cases the Gamma distribution using real data. In addition, the Exponential distribution is modified to include an extra parameter via a simple transformation using fractional mathematics. It will be shown that the modified version also exhibits Weibull characteristics for particular values of the second parameter. Full article
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2 pages, 345 KiB  
Editorial
Acknowledgement to Reviewers of Stats in 2018
by Stats Editorial Office
Stats 2019, 2(1), 32-33; https://doi.org/10.3390/stats2010003 - 11 Jan 2019
Cited by 16 | Viewed by 1652
Abstract
Rigorous peer-review is the corner-stone of high-quality academic publishing [...] Full article
17 pages, 644 KiB  
Article
The Exponentiated Burr XII Power Series Distribution: Properties and Applications
by Arslan Nasir, Haitham M. Yousof, Farrukh Jamal and Mustafa Ç. Korkmaz
Stats 2019, 2(1), 15-31; https://doi.org/10.3390/stats2010002 - 21 Dec 2018
Cited by 12 | Viewed by 2274
Abstract
In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit [...] Read more.
In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets. Full article
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14 pages, 366 KiB  
Article
Cronbach’s Alpha under Insufficient Effort Responding: An Analytic Approach
by Stephen W. Carden, Trevor R. Camper and Nicholas S. Holtzman
Stats 2019, 2(1), 1-14; https://doi.org/10.3390/stats2010001 - 20 Dec 2018
Cited by 19 | Viewed by 3800
Abstract
Surveys commonly suffer from insufficient effort responding (IER). If not accounted for, IER can cause biases and lead to false conclusions. In particular, Cronbach’s alpha has been empirically observed to either deflate or inflate due to IER. This paper will elucidate how IER [...] Read more.
Surveys commonly suffer from insufficient effort responding (IER). If not accounted for, IER can cause biases and lead to false conclusions. In particular, Cronbach’s alpha has been empirically observed to either deflate or inflate due to IER. This paper will elucidate how IER impacts Cronbach’s alpha in a variety of situations. Previous results concerning internal consistency under mixture models are extended to obtain a characterization of Cronbach’s alpha in terms of item validities, average variances, and average covariances. The characterization is then applied to contaminating distributions representing various types of IER. The discussion will provide commentary on previous simulation-based investigations, confirming some previous hypotheses for the common types of IER, but also revealing possibilities from newly considered responding patterns. Specifically, it is possible that the bias can change from negative to positive (and vice versa) as the proportion of contamination increases. Full article
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