Showing papers by "Palaniappan Vellaisamy published in 1996"
TL;DR: In this article, a subset of the given k gamma populations, with unknown scale parameters and a common known shape parameter, is selected using Gupta's subset selection procedure based on unequal sample sizes.
25 citations
TL;DR: In this paper, a new approach to the study of the distributions of sums of n Bernoulli variables by conditional distributions is considered, which leads to a characterization of binomial distribution, and provides a simple approach to study of generalized binomial distributions.
Abstract: A new approach to the study of the distributions of sums of n Bernoulli variables by conditional distributions is considered, This leads to a characterization of binomial distribution, and provides a simple approach to the study of generalized binomial distributions We show that the binomial distribution and Poisson's binomial distribution can be derived as the distribution of sum of dependent Bernoulli random variables Finally the problem of Poisson approximation to the generalized binomial distribution is investigated
19 citations
TL;DR: Upper bounds for the total variation distance, d, are derived between the distributions of two random sums of non-negative integer-valued random variables and these bounds are generally better than the known results on Poisson and compound Poisson approximations.
Abstract: We derive upper bounds for the total variation distance, d, between the distributions of two random sums of non-negative integer-valued random variables. The main results are then applied to some important random sums, including cluster binomial and cluster multinomial distributions, to obtain bounds on approximating them to suitable Poisson or compound Poisson distributions. These bounds are generally better than the known results on Poisson and compound Poisson approximations. We also obtain a lower bound for d and illustrate it with an example.
18 citations