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Discrete Distributions
The primary objective of probability models in any random experiment involves two fundamental components: the sample space and the assignment of...
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Discrete mixture representations of spherical distributions
We obtain discrete mixture representations for parametric families of probability distributions on Euclidean spheres, such as the von Mises–Fisher,...
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A Discrete Analogue of Terrell’s Characterization of Rectangular Distributions
AbstractTerrell [
18 ] showed that the Pearson coefficient of correlation of an ordered pair from a random sample of size two is at most one-half, and... -
Entropy of Some Discrete Distributions
Cheraghchi [IEEE Transactions on Information Theory, 65, 2019, 3999-4009] derived expressions for the entropy for some basic discrete distributions....
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A Family of Discrete Kernels for Presmoothing Test Score Distributions
In the fields of educational measurement and testing, score distributions are often estimated by the sample relative frequency distribution. As many...
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Families of Discrete Circular Distributions with Some Novel Applications
We give a unified treatment of constructing families of circular discrete distributions. Some of these families are deduced from established...
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On Multivariate Discrete Poisson–Lindley Distributions
Multivariate versions of five univariate Poisson–Lindley distributions are considered. These models are derived by assuming that the exponent of a...
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An Overview of Discrete Distributions in Modelling COVID-19 Data Sets
The mathematical modeling of the coronavirus disease-19 (COVID-19) pandemic has been attempted by a large number of researchers from the very...
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Standard Distributions
This chapter delves into some discrete and continuous distributions that are frequently encountered, while also examining their key characteristics.
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Bivariate Discrete Poisson–Lindley Distributions
Two families of bivariate discrete Poisson–Lindley distributions are introduced. The first is derived by mixing the common parameter in a bivariate...
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Conditional Goodness-of-Fit Tests for Discrete Distributions
In this paper, we address the problem of testing goodness-of-fit for discrete distributions, where we focus on the geometric distribution. We define...
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Discrete Tempered Stable Distributions
Discrete tempered stable distributions are a large and flexible class of models for heavy tailed and overdispersed count data. In this paper we...
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Smallest covering regions and highest density regions for discrete distributions
This paper examines the problem of computing a canonical smallest covering region for an arbitrary discrete probability distribution. This...
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Descriptive Statistics and Discrete Probability Distributions
In this chapter, we introduce several fundamental aspects of statistics: its language, quantities used to describe data, visualization of data,...
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Discrete approximations of continuous probability distributions obtained by minimizing Cramér-von Mises-type distances
We consider the problem of approximating a continuous random variable, characterized by a cumulative distribution function (cdf) F ( x ), by means of k ...
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Smooth Versus Likelihood Estimation for a Class of Mixtures of Discrete Distributions
The problem of estimating the mixing distribution Q of a power series distributions (PSD’s) mixture model is considered. In the first part of the...
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Sampling Distributions
Now, we are ready to discuss the relationship between probability and statistical inference. The two key facts to statistical inference are (a) the...
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Probability and Probability Distributions
The probability theory is considered the foundation of statistics, and R language has capability of working with probability, random variables, and...
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Multiple Random Variables and Joint Distributions
Multiple r.v.s are often involved in various random experiments. For instance, an educator might examine the joint behavior of study time and grades,...
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On a Family of Discrete Log-Symmetric Distributions
The use of continuous probability distributions has been widespread in problems with purely discrete nature. In general, such distributions are not...
