On a class of integrals involving a Bessel function times Gegenbauer polynomials.
On a zonal polynomial integral.
On some Mixture Distributions
The aim of this paper is to establish some mixture distributions that arise in stochastic processes. Some basic functions associated with the probability mass function of the mixture distributions, such as k-th moments, characteristic function and factorial moments are computed. Further we obtain a three-term recurrence relation for each established mixture distribution.
On the applications of a new technique to solve linear differential equations, with and without source.
On the compound Poisson-gamma distribution
The compound Poisson-gamma variable is the sum of a random sample from a gamma distribution with sample size an independent Poisson random variable. It has received wide ranging applications. In this note, we give an account of its mathematical properties including estimation procedures by the methods of moments and maximum likelihood. Most of the properties given are hitherto unknown.
On the computation of Aden functions
The paper deals with the computation of Aden functions. It gives estimates of errors for the computation of Aden functions by downward reccurence.
On the generalization of the STER distribution applied to generalized hypergeometric parents
On the Poisson difference distribution inference and applications.
On the product of triangular random variables
We derive the probability density function (pdf) for the product of three independent triangular random variables. It involves consideration of various cases and subcases. We obtain the pdf for one subcase and present the remaining cases in tabular form. We also indicate how to calculate the pdf for the product of n triangular random variables.
On the ratio of gamma and Rayleigh random variables
The gamma and Rayleigh distributions are two of the most applied distributions in engineering. Motivated by engineering issues, the exact distribution of the quotient X/Y is derived when X and Y are independent gamma and Rayleigh random variables. Tabulations of the associated percentage points and a computer program for generating them are also given.
On the ratio of Pearson type VII and Bessel random variables.
On the use of difference of two proportions
Differences of two proportions occur most frequently in biomedical research. However, as far as published work is concerned, only approximations have been used to study the distribution of such differences. In this note, we derive the exact probability distribution of the difference of two proportions for seven flexible beta type distributions. The expressions involve several well known special functions. The use of these results with respect to known approximations is illustrated.
Orthogonal least squares solutions for linear operators.
Orthogonality of Jacobi polynomials with general parameters.
Product Bessel distributions of the first and second kinds.
Regularization of a discrete backward problem using coefficients of truncated Lagrange polynomials.
Reliability for Beta Models
In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr(X2 < X1 ) when X1 and X2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R = Pr(X2 < X1 ) has been worked out for the majority of the well-known distributions including Normal, uniform, exponential, gamma, weibull and pareto. However, there are still many other distributions for which the form of R is...
Reliability for Laplace distributions.
Remodified Bessel functions via coincidences and near coincidences.
The beta Gumbel distribution.