The distribution of the product of two independent generalized trapezoidal random variables

ABSTRACT

In this article, we derive the probability density function (pdf) of the product of two independent generalized trapezoidal random variables having different supports, in closed form, by considering all possible cases. We also show that the results for the product of two triangular and uniform random variables follow as special cases of our main result. As an illustration, we obtain pdf of product for a suitably constrained set of parameters and plot some graphs using MATLAB, which express variation in pdf with change in different parameters of the generalized trapezoidal distribution.     

Estimation of population mean on the most recent occasion under non response in h-occasion successive sampling using several auxiliary variables

In this article, general estimation procedures of population mean on the most recent occasion in the presence of non response on all occasions have been deduced in h-occasion successive sampling. In the estimation procedures, regression type estimators have been suggested with the aid of stable and mutually independent several auxiliary variables which are readily available only on the most recent occasion. To check the efficiency of the proposed estimators, they have been compared with similar estimator in absence of non response. Properties of the suggested estimation procedures have been studied and their empirical studies are carried out to validate the theoretical results. Suitable recommendations have been made.     

On length and area-biased Maxwell distributions

This article addresses the various properties and different methods of estimation of the unknown parameter of length and area-biased Maxwell distributions. Although, our main focus is on estimation from both frequentist and Bayesian point of view, yet, various mathematical and statistical properties of length and area-biased Maxwell distributions (such as moments, moment-generating function (mgf), hazard rate function, mean residual lifetime function, residual lifetime function, reversed residual life function, conditional moments and conditional mgf, stochastic ordering, and measures of uncertainty) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimator, moments estimator, least-square and weighted least-square estimators, maximum product of spacings estimator and compare them using extensive numerical simulations. Next we consider Bayes estimation under different types of loss function (symmetric and asymmetric loss functions) using inverted gamma prior for the scale parameter. Furthermore, Bayes estimators and their respective posterior risks are computed and compared using Markov chain Monte Carlo (MCMC) algorithm. Also, bootstrap confidence intervals using frequentist approaches are provided to compare with Bayes credible intervals. Finally, a real dataset has been analyzed for illustrative purposes.     

Topp–Leone normal distribution with application to increasing failure rate data

In this article, we proposed a new three-parameter probability distribution, called Topp–Leone normal, for modelling increasing failure rate data. The distribution is obtained by using Topp–Leone-X family of distributions with normal as a baseline model. The basic properties including moments, quantile function, stochastic ordering and order statistics are derived here. The estimation of unknown parameters is approached by the method of maximum likelihood, least squares, weighted least squares and maximum product spacings. An extensive simulation study is carried out to compare the long-run performance of the estimators. Applicability of the distribution is illustrated by means of three real data analyses over existing distributions.     

A comparative study of correlation coefficients in spatially MRSI-observed neurochemicals from multiple sclerosis patients

In measuring the association between magnetic resonance spectroscopic imaging (MRSI)-observed neurochemicals from multiple sclerosis (MS) patients, the classic correlation coefficients such as the Pearson's r, Spearman's ρand Kendall's τdo not take into account the spatial dependence of the observations. This paper reports a comparative study on these classic correlation coefficients (Pearson's r, Spearman's ρand Kendall's τ) and some more recent correlation coefficients (Tjostheim's a, the modified t) that take into account the spatial dependence of the intensities of the concentrations of several neurochemicals in MS patients. Our study indicates that the use of the classic correlation coefficients that ignores the spatial dependence of the observations may overestimate the statistical significance of the results.     

Corporate planning in domestic airlines— An Indian case study

In this article the author considers the problems of planning in the airline industry, drawing specifically on experience in the domestic Indian airline. The article seeks to examine some of the strategic issues relevant to domestic airlines which, while related here to the Indian environment, may be seen to be pertinent in most developing countries.