M. Masoom Ali

On order statistics from the log-logistic distribution

Abstract Recurrence relations for negative and fractional moments of single order statistics and product and quotient moments of two order statistics drawn from log-logistic distribution have been obtained.

Some Exponentiated Distributions

In this paper we study a number of new exponentiated distributions. The survival function, failure rate and moments of the distributions have been derived using certain special functions. The behavior of the failure rate has also been studied.

A truncated Pareto distribution

Modeling problems in communication networks predominantly involve long-tailed distributions. These distributions, however, suffer from the weakness of not having finite moments of all orders and this weakness has restricted their use in communication networks. In this note, we introduce a truncated version of the Pareto distribution - the most commonly known long-tailed distribution - which possesses finite moments of all orders and could therefore be a better model for communication networks. Explicit expressions for the moments are derived for the truncated distribution.

Characterization of probability distributions through higher order gap

Weibull, Burr, Pareto and power function distributions have been characterized through the conditional moments of order statistics with higher gap and some of its important deductions are discussed.

Estimation and testing of P(Y > X) in two-parameter exponential distributions

In this article, we obtain the UMVUE of the reliability function ξ=P(Y>X) and the UMVUE of ξ k =[P(Y>X)] k in the two-parameter exponential distributions with known scale parameters. We also derive the distribution of the UMVUE of ξ and further considering the tests of hypotheses regarding the reliability function ξ.

A Class of Poisson Mixtured Distributions

Abstract In this paper, a class of mixtured distributions is defined which is known as “Poisson mixture of distributions”. Some characteristics of these distributions are then provided.

Some skew symmetric inverse reflected distributions

Skew-symmetric distributions are defined based on the reflected gamma, reflected Weibull and the reflected Pareto distributions. Expressions are derived for the probability density function, cumulative distribution functions, moments and the shape. Estimation procedures by the methods of moments and maximum likelihood and Fisher information matrices are provided. Evidence of flexibility of the distributions is shown. An application is illustrated using the Old Faithful Geyser data. Some of the attractive properties of the distributions include multimodality and polynomial tails.

Information matrices for normal and Laplace mixtures

The Fisher information matrices (FIMs) are derived for a mixture of two Laplace distributions and a mixture of two normal distributions. The expressions for the matrices involve the Lerch function. Practical application of the results is illustrated through two published works on aircraft navigation and borehole geophysics.

ESTIMATING THE QUANTILE FUNCTION OF A LOCATION-SCALE FAMILY OF DISTRIBUTIONS BASED ON FEW SELECTED ORDER STATISTICS

Some general asymptotic methods of estimating the quantile function, Q(ξ), 0<ξ<1, of location-scale families of distributions based on a few selected order statistics are considered, with applications to some nonregular distributions. Specific results are discussed for the ABLUE of Q(ξ) for the location-scale exponential and double exponential distributions. As a further application of the exponential results, we discuss a nonlinear estimator of Q(ξ) for the scale-shape Pareto distribution.

The distribution of sums, products and ratios for Lawrance and Lewis's bivariate exponential random variables

We derive the exact distributions of R=X+Y, P=XY and W=X/(X+Y) and the corresponding moment properties when X and Y follow Lawrence and Lewiss bivariate exponential distribution. The expressions turn out to involve special functions. We also provide extensive tabulations of the percentage points associated with the distributions. These tables-obtained using intensive computing power-will be of use to practitioners of the bivariate exponential distribution.