Related papers: On a six-parameter generalized Burr XII distributi…
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
The paper deals with a generalisation of uniform distribution. The analogues of Weyl's criterion are derived.
In the present paper a generalization of Gurland distribution [3] is obtained as a beta mixture of the generalized Poisson distribution (GPD) of Consul and Jain [2]. The first two moments of the distribution and a recurrence relation among…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
In this article, a generalized version of Negative binomial-beta exponential distribution with five parameters have been introduced. Some interesting submodels have been derived from it. A comprehensive mathematical treatment of proposed…
Four new probability models are derived which generalize the common univariate continuous distributions. Classical distributional measures are derived from Hoel, et al., Introduction to Probability Theory, 1971. Measures include probability…
A new generalization of the family of Poisson-G is called beta Poisson-G family of distribution. Useful expansions of the probability density function and the cumulative distribution function of the proposed family are derived and seen as…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
The aim of this article is to determine a new six-parameter Beta Weibull distribution and its various associated functions, namely the cumulative distribution, survival, probability density and hazard functions. Next, we determine the…
From a new class of q-deformed coherent states we introduce a generalization of the Euler probability distribution for which the main statistical parameters are obtained explicitly. As application, we discuss the corresponding photon…
The distribution of the sum of r-th power of standard normal random variables is a generalization of the chi-squared distribution. In this paper, we represent the probability density function of the random variable by an one-dimensional…
This study introduces a new family of probability distributions, termed the alpha power Harris-generalized (APHG) family. The generator arises by incorporating two shape parameters from the Harris-G framework into the alpha power…
We develop a fractional extension of the classical binomial distribution and the associated Bernstein operator, formulated within the framework of the generalized binomial theorem (Hara and Hino [Bull.\ London Math.\ Soc. \textbf{42}…
The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…
We derive the exact probability density function of the product of $N$ independent variance-gamma random variables with zero location parameter. We then apply this formula to derive formulas for the cumulative distribution function and…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
We compute the distribution of the purity for random density matrices (i.e.random mixed states) in a large quantum system, distributed according to the Bures measure. The full distribution of the purity is computed using a mapping to random…
Based on cumulative distribution functions, Fourier series expansion and Kolmogorov tests, we present a simple method to display probability densities for data drawn from a continuous distribution. It is often more efficient than using…