A generalized probability distribution is developed which served as a general formula for some well known probability distributions such as weibull, exponential, rayleigh. gamma, log-nonnal. pareto. maxwell, generalized laplace etc. Besides aforesaid probahility distributions, a family of new disuibutions can also be derived from it. The statistical properties viz. moments and moment generating...

Abstract All statistical measurements which represent the values of useful unknown quantities have a realm that is both finite and discrete. Thus our uncertainties about any measurement can be represented by discrete probability mass functions. Nonetheless, common statistical practice treats probability distributions as representable by continuous densities or mixture densities. Many statistica...

In the paper, authors establish an inequality involving exponential functions and sums, introduce a ratio of finitely many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete Bernstein function property, newly introduced ratio, construct two inequalities multinomial coefficients multivariate beta functions.

We show that the generating functions of the generalized Catalan numbers can be identified with the moment generating functions of probability density functions related to the Brownian motion stochastic process. Specifically, the probability density functions are exponential mixtures of inverse Gaussian (EMIG) probability density functions, which arise as the first passage time distributions to...

In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of equations. addition, finding solutions obtained equations, probability characteristics are examined. The version transformation method (DTM) is used to obtain an analytical solution close equation. Approximate expected value...

Measurement and modelling of distributions of data communication times is commonly done for telecommunication networks, but this has not previously been done for message passing communications on parallel computers. We have used the MPIBench program to measure distributions of point-to-point MPI communication times for two different parallel computers, with a low-end Ethernet network and a high...

In this paper, the reconcilability between the P-value and the posterior probability in testing a point null hypothesis against the one-sided hypothesis is considered. Two essential families, non regular and exponential family of distributions, are studied. It was shown in a non regular family of distributions; in some cases, it is possible to find a prior distribution function under which P-va...