Adnan M. Awad

Estimation of p(y<x) in the burr case: a comparative study

This paper provides a simulation study which compares three estimators for R = P(Y<X) when Y and X are two independent but not identically distributed Burr random variables. These estimators are the minimum variance unbiased, the maximum likelihood and Bayes estimators. Moreover, the sensitivity of Bayes estimator to the prior parameters is considered.

Some inference results on pr(x < y) in the bivariate exponential model

This paper provides three different estimators for Pr(X < Y) when X and Y have a bivariate exponential distribution. The asymptotic variances of the three estimators are also derived. A test for the equality of the means of X and Y and confidence limits for the difference of the two means are presented. Our results are directly applicable in a reliability context with underlying bivariate exponential distribution.

Prediction intervals for the future record values from exponential distribution: comparative study

!n this paper we consider the predicf an problem of the future nth record value based an the first m (m < n) observed record values from one-parameter exponential distribution. We introduce four procedures for obtaining prediction intervals for the nth record value. The performance of the so obtained intervals is assessed through numerical and simulation studies. In these studies, we provide the means and standard errors of lower limits. upper limits and lengths of prediction intervals. Further, we check the validation of these intervals based on some point predictors.

Properties of the Akaike information criterion

The paper gives the origins of AIC and discusses the main properties of this measure when it is applied to continuous and discrete models. It is illustrated that AIC is not a measure of informativity because it fails to have some expected properties of information measures. Some modifications of AIC are pointed out together with their advantages over AIC.

A note on characterization based on shannon entropy of record statistics

In this note we compare the Shannon entropy of record statistics with the Shannon entropy of the original data and give an application to characterization of the generalized Pareto distribution,

Normality Test Based on a Truncated Mean Characterization

This article generalizes a characterization based on a truncated mean to include higher truncated moments, and introduces a new normality goodness-of-fit test based on the truncated mean. The test is a weighted integral of the squared distance between the empirical truncated mean and its expectation. A closed form for the test statistic is derived. Assuming known parameters, the mean and the variance of the test are derived under the normality assumption. Moreover, a limiting distribution for the proposed test as well as an approximation are obtained. Also, based on Monte Carlo simulations, the power of the test is evaluated against stable, symmetric, and skewed classes of distributions. The test proves compatibility with prominent tests and shows higher power for a wide range of alternatives.

Entropy measures and some distribution approximations

Abstract Many information measures are suggested in the literature. Among these measures are the Shannon H n ( θ ) and the Awad A n ( θ ) entropies. In this work we suggest a new entropy measure, B n ( θ ), which is based on the maximum likelihood function. These three entropies were calculated from the gamma distribution and its normal approximation, the binomial and its Poisson approximation, and the Poisson and its normal approximation. The relative losses in these three entropies are used as a criterion for the appropriateness of the approximation.

On the Fisher Information

Abstract This paper gives some comments and drawbacks of the Fisher information together with some new properties of this measure of information. A modification of the Fisher information is suggested. Some properties of the modified measure are given.

Large sample prediction intervals for a future sample mean: A comparative study

This article gives a comparative study among several prediction intervals for the future sample mean. The observed sample, used in the techniques and the future sample for which the prediction intervals were established share the same underlying distribution. Two assumed underlying distributions were used. The first underlying distribution is the exponential with parameter θ. Five different intervals were set for the prediction of the future sample mean. The second underlying distribution is the normal with the parameter θ as the common value for the mean and the variance. Seven intervals were compared. A simulation validation was done. Some criteria were set for the “best” interval in both cases. Moreover, the merits of the techniques were given, and a table of results of the simulations is supplied.

Large sample prediction intervals for future geometric mean. A comparative study

This paper provides simulation comparisons among the perfor-mance of 11 possible prediction intervals for the geometric mean of a Pareto distribution with parameters (λ,β). Six different procedures were used to obtain these intervals, namely true inter-val, pivotal interval, maximum likelihood estimation interval, central limit theorem interval, variance stabilizing interval and a mixture of the above intervals. Some of these intervals are valid if the observed sample size n is large, others are valid if both, n and the future sample size m, are large. Some of these intervals require a knowledge of λ or β, while others do not. The simulation validation and efficiency study shows that intervals depending on the MLEs are the best. The second best intervals are those obtained through pivotal methods or variance stabilization transformations. The third group of intervalsis that which depends on the central limit theorem when A i s known. There are two intervals which proved to be unacceptable under any crite...