Mohammad Ahsanullah

Generalized order statistics from exponential distribution

In this paper some distributional properties of the generalized order statistics from two parameter exponential distribution are given. The minimum variance linear unbiased estimators of the parameters and an important characterization of the exponential distribution are presented.

Recurrence relations for single and product moments of record values from generalized pareto distribution

In this paper we establish some recurrence relations satisfied by single and product moments of upper record values from the generalized Pareto distribution. It is shown that these relations may be used to obtain all the single and product moments of all record values in a simple recursive manner. We also show that similar results established recently by Balakrishnan and Ahsanullah (1993) for the upper record values from the exponential distribution may be deduced by letting the shape parameter p tend to 0.

A Characterization of the Uniform Distribution by Dual Generalized Order Statistics

Abstract Some distributional properties of lower generalized order statistics are presented. A characterization of the uniform distribution based on the lower generalized order statistics is given.

Normal and Student's t Distributions and Their Applications

The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.

An introduction to order statistics

Basic definitions.- Distributions of order statistics.- Sample quantiles and ranges.- Representations for order statistics.- Conditional distributions of order statistics.-Order statistics for discrete distributions.- Moments of order statistics: general relations.- Moments of uniform and exponential order statistics.- Moment relations for order statistics: normal distribution.- Asymptotic behavior of the middle and intermediate order statistics.- Asymptotic behavior of the extreme order statistics.- Some properties of estimators based on order statistics.- Minimum variance linear unbiased estimators.- Minimum variance linear unbiased estimators and predictors based on censored samples.- Estimation of parameters based on fixed number of sample quantiles.- Order statistics from extended samples.- Order statistics and record values.- Characterizations of distributions based on properties of order statistics.- Order statistics and record values based on Falpha distributions.- Generalized order statistics.- Compliments and problems.

Record values and the exponential distribution

A sequence {Xn,n≧1} of independent and identically distributed random variables with continuous cumulative distribution functionF(x) is considered.Xj is a record value of this sequence ifXj>max (X1, …,Xj−1). Let {XL(n) n≧0} be the sequence of such record values. Some properties ofXL(n) andXL(n)−XL(n−1) are studied when {Xn,n≧1} has the exponential distribution. Characterizations of the exponential distribution are given in terms of the sequence {XL(n),n≧0}

ESTIMATION OF PARAMETERS OF THE GENERALIZED GEOMETRIC DISTRIBUTION USING RANKED SET SAMPLING

The estimates of the parameters of the generalized geometric distribution are obtained by using ranked set sampling procedure. These estimates are compared with the ordered least squares estimates given by Downton (1954, Annals of Mathematical Statistics 25, 303-316). It is shown that the relative precisions of our estimators are higher than those of the ordered least squares estimators. Furthermore, the relative precision of our estimator for the population mean is higher than the usual estimator based on ranked set sampling.

Relations for single and product moments of record values from Gumbel distribution

In this paper some recurrence relations between the moments of record values from the Gumbel distribution are established. It is shown that using these recurrence relations, all the single and product moments of all record values can be obtained in a very simple recursive process.

Recurrence relations for moments of record values from generalized extreme value distribution

In this paper some recurrence relations between the moments of record values from the generalized extreme value distribution are established. It is shown that using these recurrence relations, all the single and product moments of all record values can be obtained in a simple recursive manner.

Generalized order statistics from two parameter uniform distribution

In this paper some distributional properties of the generalized order statistics from uniform distribution are given. The minimum variance linear unbiased as well best ( in the sense of minimum mean squared error) invariant estimators of the parameters of the two parameter uniform distribution based on the first m generalized order statistics are presented.