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Joint Distributions
This chapter introduces the distribution of functions of several random variables. The Jacobian of matrix transformation is described and its...
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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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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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Bivariate Sarmanov Phase-Type Distributions for Joint Lifetimes Modeling
In this paper, we are interested in the dependence between lifetimes based on a joint survival model. This model is built using the bivariate...
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Analytical Computation of Pseudo-Gibbs Distributions for Dependency Networks
Dependency network (DN) aims at using a collection of conditional distributions to identify a joint pdf. When the DN is compatible (self-consistent),...
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Bayesian ridge estimators based on copula-based joint prior distributions for regression coefficients
Ridge regression is a widely used method to mitigate the multicollinearly problem often arising in multiple linear regression. It is well known that...
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On connections between skewed, weighted and distorted distributions: applications to model extreme value distributions
The purpose of the paper is to explore the connections between skew symmetric, weighted and distorted univariate distributions as well as how they...
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Flexible asymmetric multivariate distributions based on two-piece univariate distributions
Classical symmetric distributions like the Gaussian are widely used. However, in reality data often display a lack of symmetry. Multiple...
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Joint Models for Longitudinal Zero-Inflated Overdispersed Binomial and Normal Responses
In this paper, we propose joint random effects models for longitudinal mixed overdispersion binomial and normal responses where the overdispersion...
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Distortion representations of multivariate distributions
The univariate distorted distributions were introduced in risk theory to represent changes (distortions) in the expected distributions of some risks....
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Bivariate Extreme Value Distributions
The title of this chapter is deliberately chosen to focus on the bivariate case instead of the general multivariate. The reason is mainly one of...
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Probability Distributions
To the uninitiated, a stochastic model may seem to emerge from nowhere with little explanation. This chapter attempts to address the information gap...
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Analyzing quantitative performance: Bayesian estimation of 3-component mixture geometric distributions based on Kumaraswamy prior
This research addresses the underutilization of discrete life testing models and proposes a Bayesian estimation strategy for a 3-component mixture of...
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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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On Some Characterizations of Probability Distributions Based on Maxima or Minima of Some Families of Dependent Random Variables
Most of the characterizations of probability distributions are based on properties of functions of possibly independent random variables. We...
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Gaussian Distributions
This chapter is concerned with Gaussian distributions, either real Gaussian on...
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Identifiability of Asymmetric Circular and Cylindrical Distributions
Identifiability of statistical models is a fundamental and essential condition that is required to prove the consistency of maximum likelihood...
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Confidence distributions and hypothesis testing
The traditional frequentist approach to hypothesis testing has recently come under extensive debate, raising several critical concerns. Additionally,...
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Flexible Clustering with a Sparse Mixture of Generalized Hyperbolic Distributions
Robust clustering of high-dimensional data is an important topic because clusters in real datasets are often heavy-tailed and/or asymmetric....
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Bayesian joint quantile autoregression
Quantile regression continues to increase in usage, providing a useful alternative to customary mean regression. Primary implementation takes the...
