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The Multivariate Power-Gamma Distribution Using Factor Analysis Models
Moments and the moment-generating function of the univariate power-gamma distribution are obtained. This distribution was proposed elsewhere when a...
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Functions of Random Variables
This chapter discusses single random variables and its transforms. Various types of transformations such as sum, squares, square-roots,...
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A Generalized Multivariate Gamma Distribution
In this chapter, we introduce a multivariate gamma distribution whose marginals are finite mixtures of gamma distributions and correlation between...
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Goodness-of-fit procedure for gamma processes
Gamma processes are commonly used for modelling the accumulative deterioration of systems, in many fields. However, given a series of observations,...
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Testing omitted variables in VARs
A procedure is outlined aiming at testing the bias due to omitted variables in vector autoregressions. The procedure consists first of filtering a...
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Functional Principal Component Analysis for Multiple Variables on Different Riemannian Manifolds
Functional principal component analysis (FPCA) is a very important dimension reduction tool for functional data analysis. The conventional FPCA...
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Bayesian Estimation for Bivariate Gamma Processes with Copula
Gamma stochastic process has been proposed to replace Brownian motion and geometric Brownian motion to characterize the degradation measurements from...
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Expectation identities from integration by parts for univariate continuous random variables with applications to high-order moments
Inspired by the Conjugate Variables Theorem in physics, we provide a general expectation identity for univariate continuous random variables by...
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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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Random Variables
Based on the description of probability in Chap. 2 , let us now introduce and discuss several topics on random...
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Introduction to Inferential Statistics 1: Random Variables
Inferential statistics aim at deriving generalized statements about a population based on data of a given sample of that population (see also Chap....
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Multiple combined gamma kernel estimations for nonnegative data with Bayesian adaptive bandwidths
The modified (or second version) gamma kernel of Chen [ Probability density function estimation using gamma kernels , Annals of the Institute of...
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Variants of non-symmetric correspondence analysis for nominal and ordinal variables
Non-symmetric correspondence analysis (NSCA) is a multivariate data analysis technique that has gained increasing attention in recent years. NSCA is...
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Small Area Models for Non-normal Response Variables
As introduced in Chap. 4, the basic small area models are based on normality assumption for the response variables.
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Kernel regression for errors-in-variables problems in the circular domain
We study the problem of estimating a regression function when the predictor and/or the response are circular random variables in the presence of...
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Simulation Study of Estimators of the Gamma Rate Parameter Using MLE as a Baseline Estimator
Classical estimation methods of the rate parameter of the gamma distribution have shown to have quality issues. In this paper we propose three...
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Scan Statistics for Integer-Valued Random Variables: Conditional Case
In this chapter, we review approximations and inequalities for the distribution of conditional scan statistics for a sequence of independent and...
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Housing variables and immigration: an exploratory analysis in New York City
The relationship between housing and immigration has become relevant in the U.S., especially in a highly populated metropolis such as New York City....
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Stochastic Comparisons of Weighted Sums of Random Variables
Let X = (X 1, …, X n) be a random vector of observations which may not be independent or identically distributed, and let...