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On Extremes of Two-Dimensional Student-t Distribution of the Marshall–Olkin Type
Although there are some results related to classical bivariate Student- t distribution, studying the exact distribution of its extremes is not so...
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Poisson Distribution
After finishing the chapter, readers will be able to …...
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A copula-based approximation to Markov chains
The Markov chain is well studied and widely applied in many areas. For some Markov chains, it is infeasible to obtain the explicit expressions of...
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Chapter 7: Rectangular Matrix-Variate Distributions
Thus far, we have primarily been dealing with distributions involving real positive definite or Hermitian positive definite matrices. Rectangular...
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Coupling Poisson Processes by Self-Decomposability
We analyze a method to produce pairs of non-independent Poisson processes M ( t ), N ( t ) from positively correlated, self-decomposable, exponential...
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Copula Theory: An Introduction
In this survey we review the most important properties of copulas, several families of copulas that have appeared in the literature, and which have...
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Exact Simulation of Solutions of SDEs
Accurate scenario simulation methods for solutions of multi-dimensional stochastic differential equations find applications in the statistics of...
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Mathematical Properties of the Multivariate t Distribution
The known mathematical properties of the multivariate t distribution are reviewed. We believe that this review will serve as an important reference...
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Models for Recurrent Events in Reliability and Survival Analysis
Existing models forrecurrent phenomena occurring in public health, biomedicine, reliability, engineering, economics, and sociology are reviewed. A...
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Applications in Risk Management
This chapter discusses applications of Monte Carlo simulation to risk management. It addresses the problem of measuring the risk in a portfolio of...
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Asymmetric Multivariate Laplace Distribution
In this chapter we present the theory of a class of multivariate laws that we term asymmetric Laplace (AL) distributions [see Kozubowski and...
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Classical Symmetric Laplace Distribution
In the course of our study of the Laplace distribution and its generalizations we have noticed that quite often in the statistical literature this...
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Statistical tests based on empirical processes and related questions
We consider goodness-of-fit tests for hypotheses about the forms of distributions and their membership in prescribed families of distributions. We...
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Analysis of Variance and Experimental Design
Analysis of variance can be viewed as a special case of multiple regression where the explanatory variables are entirely qualitative. In the previous...
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A Conversation with Ingram Olkin
Early in 1986, a new journal Statistical Science of the Institute of Mathematical Statistics appeared. This is a journal Ingram Olkin was intimately...