N. Balakrishnan

A first course in order statistics

Basic Distribution Theory Discrete Order Statistics Order Statistics from Some Specific Distributions Moment Relations, Bounds, and Approximations Characterizations Using Order Statistics Order Statistics in Statistical Inference Asymptotic Theory Record Values Bibliography Indexes.

Continuous Multivariate Distributions

In this article, we present a concise review of developments on various continuous multivariate distributions. We first present some basic definitions and notations. Then, we present several important continuous multivariate distributions and list their significant properties and characteristics. Keywords: generating function; moments; conditional distribution; truncated distribution; regression; bivariate normal; multivariate normal; multivariate exponential; multivariate gamma; dirichlet; inverted dirichlet; liouville; multivariate logistic; multivariate pareto; multivariate extreme value; multivariate t; wishart translated systems; multivariate exponential families

Order statistics and inference : estimation methods

List of Tables. List of Figures. Introduction. Basic Theory. Moments and Other Expected Values. Linear Estimation Based on Order Statistics. Maximum Likelihood Estimation. Approximate Maximum Likelihood Estimation. Optimal Linear Estimation Based on Selected Order Statistics. Cohen -Whitten Estimators: Using Order Statistics.Estimation in Regression Models. A Sample Completion Technique for Censored Samples. Bibliography. Index.

Continuous bivariate distributions

Univariate distributions. - Bivariate copulas. - Distributions expressed as copulas. - Concepts of stochastic dependence. - Measures of dependence. - Constructions of bivariate distributions.- Bivariate distributions constructed by conditional approach. - Variables in common method. - Bivariate gamma and related distributions. - Simple forms of the bivariate density function. - Bivariate exponentional and related distributions. - Bivariate normal distribution. - Bivariate extreme value distributions. - Elliptically symmetric bivariate distributions and other symmetric distributions. - Simulation of bivariate observations.

A Simple Simulational Algorithm for Generating Progressive Type-II Censored Samples

Abstract We establish an independence result concerning a progressive Type-II censored sample from the uniform distribution. This result is used to present a simple and efficient simulational algorithm for generating a progressive Type-II censored sample from any continuous distribution.

Interval estimation of parameters of life from progressively censored data

A conditional method of inference is used to derive exact confidence intervals for several life characteristics such as location, scale, quantiles, and reliability when the data are Type II progressively censored. The method is shown to be feasible and practical, although a computer program may be required for its implementation. The method is applied for the purpose of illustration to the extreme-value and the one- and two-parameter exponential models. Prediction limits for the lifelength of future units are also discussed. An example consisting of data from an accelerated test on insulating fluid reported by Nelson is used for illustration and comparison.

Skewed multivariate models related to hidden truncation and/or selective reporting

The univariate skew-normal distribution was introduced by Azzalini in 1985 as a natural extension of the classical normal density to accommodate asymmetry. He extensively studied the properties of this distribution and in conjunction with coauthors, extended this class to include the multivariate analog of the skew-normal. Arnold et al. (1993) introduced a more general skew-normal distribution as the marginal distribution of a truncated bivariate normal distribution in whichX was retained only ifY satisfied certain constraints. Using this approach more general univariate and multivariate skewed distributions have been developed. A survey of such models is provided together with discussion of related inference questions.

Acceptance Sampling Plans from Truncated Life Tests Based on the Generalized Birnbaum–Saunders Distribution

In this article, we develop acceptance sampling plans when the life test is truncated at a pre-fixed time. The minimum sample size necessary to ensure the specified median life is obtained by assuming that the lifetimes of the test units follow a generalized Birnbaum–Saunders distribution. The operating characteristic values of the sampling plans as well as producers risk are presented. Two examples are also given to illustrate the procedure developed here, with one of them being based on a real data from software reliability.

Estimation of parameters from progressively censored data using EM algorithm

EM algorithm is used to determine the maximum likelihood estimates when the data are progressively Type II censored. The method is shown to be feasible and easy to implement. The asymptotic variances and covariances of the ML estimates are computed by means of the missing information principle. The methodology is illustrated with two popular models in lifetime analysis, the lognormal and Weibull lifetime distributions.

A General Purpose Approximate Goodness-of-Fit Test

Skewed distributions play an important role in the analysis of data from quality and reliability experiments. Very often unknown parameters must be estimated from the sample data in order to test whether the data has come from a certain family of distri..