Zeinhum F. Jaheen

Statistical inference for the Burr model based on progressively censored data

Abstract Maximum likelihood and Bayes estimates for the two parameters and the reliability function of the Burr Type XII distribution are obtained based on progressive Type II censored samples. An approximation based on the Laplace approximation method developed by Tierney and Kadane [1] and a bivariate prior density for the two unknown parameters, suggested by Al-Hussaini and Jaheen [2] are used for obtaining the Bayes estimates. These estimates are compared via Monte Carlo simulation study.

Empirical Bayes estimation of P(Y < X) and characterizations of Burr-type X model

This paper deals with the estimation of R = P(Y < X) when Y and X are two independent but not identically distributed Burr-type X random variables. Maximum likelihood, Bayes and empirical Bayes techniques are used for this purpose. Monte-Carlo simulation is carried out to compare the three methods of estimation. Also, two characterizations of the Burr-type X distribution are presented. The first characterization is based on the recurrence relationships between two successively conditional moments of a certain function of the random variable, whereas the second one is given by the conditional variance of that function.

Bayesian estimation of the parameters,reliability and failure rate functions of the burr type xii failure model

Based on a type-2 censored sample of the life times from a two parameter Burr type-XII failure time model, the Bayes estimates of the two (unknown) parameters, the reliability and failure rate functions are obtained by using Bayes approximation form due to Lindley (1980). The estimated risks of the Bayes estimates are computed and compared with the corresponding estimated risks of the maximum likelihood estimates.

Bayesian prediction bounds for the burr type XII failure model

In this paper, the problem of predicting the future observations from the Burr type XII distribution, based on the past observations having the same distribution, is considered from a Bayesian approach One sample and a ser ies of M+l samples techniques are used in this article based on a bivariate prior density suggested by AL.-Hussaini and Jaheen (1992). Numerical examples are used to illustrate the procedures.

Estimation Based on Generalized Order Statistics from the Burr Model

ABSTRACT The concept of generalized order statistics was introduced by Kamps (1995) to unify several concepts that have been used in statistics such as order statistics, record values, and sequential order statistics. Estimation of the parameters of the Burr type XII distribution are obtained based on generalized order statistics. The maximum likelihood and Bayes methods of estimation are used for this purposes. The Bayes estimates are derived by using the approximation form of Lindley (1980). Estimation based on upper records from the Burr model is obtained and compared by using Monte Carlo simulation study. Our results are specialized to the results of AL-Hussaini and Jaheen (1992) which are based on ordinary order statistics.

Empirical Bayes Inference for Generalized Exponential Distribution Based on Records

Abstract Record values can be viewed as order statistics from a sample whose size is determined by the values and the order of occurrence of observations. Bayes and empirical Bayes estimators for the unknown parameter of the generalized exponential distribution are derived based on record statistics. These estimates are obtained based on squared error and LINEX loss functions. Prediction bounds for future lower record values are obtained by using Bayes and empirical Bayes techniques. Numerical example is given to illustrate the results.

A Bayesian analysis of record statistics from the Gompertz model

The Gompertz distribution has been used as a growth model and it can be used to fit tumor growth. Record values can be viewed as order statistics from a sample whose size is determined by the values and the order of occurrence of observations. Based on record values from the two-parameter Gompertz distribution, Bayes estimators for the two unknown parameters are obtained by using Laplace approximation. These estimates are obtained based on the squared error and LINEX loss functions. Predictions for future upper record values from the Gompertz model are obtained from a Bayesian approach. The maximum likelihood and Bayes estimates are compared via Monte Carlo simulation study and a numerical example is given to illustrate the results of prediction.

Bayesian prediction bounds for the Burr type XII distribution in the presence of outliers

Abstract Bayesian prediction bounds for some order statistics of future observations from the Burr (c, k) distribution are obtained in the presence of single outlier arising from different members of the same family of distributions. Single outliers of types kk0 and k + k0 are considered and a bivariate prior density for c and k as suggested by AL-Hussaini and Jaheen (J. Statist. Comp. and Simulation 41 (1992)) is used.

Bayesian one-sample prediction of future observations under Pareto distribution

Suppose that the length of time in years for which a business operates until failure has a Pareto distribution. Let t 1 < t 2 < ··· < t r denote the survival lifetimes of the first r of a random sample of n businesses. Bayesian predictions are to be made on the ordered failure times of the remaining (n − r) businesses, using the conditional probability function. Numerical examples are given to illustrate our results.

Approximate Bayes estimators applied to the Burr model

This paper extends the results of AL-Hussaini and Jaheen (1992) and develops approximate Bayes estimators of the two (unknown) parameters, reliability and failure rate functions of the Burr type XII failure model by using the method of Tierney and Kadane (1986) based on type-2 censored samples. Comparisons are made between those estimators and their corresponding Bayes estimators obtained by using the method of Lindley (1980) together with the maximum likelihood estimators based on Monte Carlo simulation study.