Intro
Life and Works of Barry C. Arnold
Publications of Barry C. Arnold
Books
Books Edited
Papers
Preface
Contents
Contributors
About the Editors
Part I Ordered Data Analysis
A Record-Based Transmuted Family of Distributions
1 Introduction
2 Transmuted Distributions
3 Record-Based Transmuted Distributions
4 Special Cases
4.1 Record-Based Transmuted Uniform Distribution
4.2 Record-Based Transmuted Exponential Distribution
4.3 Record-Based Transmuted Linear-Exponential Distribution
4.4 Record-Based Transmuted Weibull Distribution

4.5 Record-Based Transmuted Normal Distribution
4.6 Record-Based Transmuted Logistic Distribution
5 Dual Record-Based Transmuted Distributions
6 Concluding Remarks
References
Large-Sample Properties of Jackknife Estimators of the Variance of a Sample Quantile
1 Introduction
2 Preliminaries
2.1 Jackknife Estimators of Variance of an Estimator
2.2 Joint Limit Distribution of Spacings in a Neighborhood
3 Delete-d Jackknife Estimators of the Variance of Xk:n
3.1 The Central Case
3.2 Intermediate Case

4 Delete-d Jackknife Estimator of the Variance of the Sample Median
5 Concluding Remarks
References
Properties of System Lifetime in the Classical Model with I.I.D. Exponential Component Lifetimes
1 Introduction and Auxiliary Results
2 Density Function
3 Failure Rate
4 Mean Residual Lifetime
References
Part II Univariate Distribution Theory
A Note on the Product of Independent Beta Random Variables
1 Introduction
2 Approximations Based on Mixtures
2.1 Mixtures of Generalized Gamma Distributions
2.2 A Single Beta or a Mixture of Two Beta Distributions

2.3 Mixtures of Gamma Distributions: Type I
2.4 Mixtures of Gamma Distributions: Type II
3 Simulation Study
4 Concluding Remarks
References
On the Distribution of the Product of Independent Beta Random Variables
Applications
1 Introduction
2 Some Results Concerning Ratios of Gamma Functions
3 Main Results Concerning the Exact Distribution of the Product of Independent Beta Random Variables
3.1 The General Case
3.2 The Particular Case of All Different Sets of Pairs of Parameters
3.3 The Particular Case of All Equal Sets of Pairs of Parameters

3.4 The Distribution of the Product of Powers of Independent Beta Random Variables
4 The Practical Implementation of the Exact Distribution in Sect. 3
Another Look at the Exact Distribution on the Way to Near-Exact Distributions
5 Near-Exact Distributions for the Product of Independent Beta Random Variables
5.1 Near-Exact Distributions for Z in (2)
5.2 Near-Exact Distributions for the Product of Independent Beta Random Variables Raised to Different Powers
6 Some Evidence Better Analyzed from Numerical Studies
7 Applications