New Trends in Discrete Probability and Statistics
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".
Deadline for manuscript submissions: 30 September 2024 | Viewed by 1222
Special Issue Editor
Interests: Bahadur efficiency; orthogonal polynomials and functions of hypergeometric types (Jacobi, Laguerre, Hermite, Askey scheme, etc.); Fourier series in special orthogonal functions; asymptotic properties of parametric tests; applications of statistics to biology and medical sciences; directional data; spatial statistics
Special Issue Information
Dear Colleagues,
The status of discrete statistics within the field of mathematical statistics is multiple and somewhat paradoxical. Most of the time, the collection of real data yields discrete empirical distributions. However, continuous models have received more attention, and consequently, more development than discrete ones. A first reason was already pointed out by Kendall and Stewart in their classic, The Advanced Theory of Statistics: ”In the ordinary data of experience our distributions are invariably discontinuous, because our measurements can only attain a certain degree of accuracy”; however, ”continuous distributions are generally amenable to more elegant mathematical treatment than are discrete distributions.” In their more recent encyclopedic book, Univariate Discrete Distributions, Johnson et al. confirmed this state of affairs: ”Goodness-of-fit tests for discrete distributions have not been researched as extensively as continuous distributions”. However, new prospects for discrete statistics are on the agenda, in the same way as how A. Terras describes for a Fourier analysis on groups and applications the renewal of discrete geometry: ”In this age of computer, it is very natural to replace the continuous with the finite. (...) Here in finite land, we will have no worries about convergence of integrals or interchange of summation and integration. Such worries often obscured the continuous theory in a myriad of analytical details.” Our aim is to illustrate these various aspects by means of different tools.
Dr. Jean Renaud Pycke
Guest Editor
Manuscript Submission Information
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Keywords
- parametric discrete distributions
- distributions associated with discrete orthogonal polynomials
- empirical distributions
- empirical processes
