Related papers: A note on sum and difference of correlated chi-squ…
Many types of bounded data defined on the unit interval arise naturally as ratios of the form $X/(X + Y)$. In the existing literature, the main statistical models proposed for this type of bounded data typically based on the assumption that…
In this paper, we obtain an upper bound for the Gini mean difference based on mean, variance and correlation for the case when the variables are correlated. We also derive some closed-form expressions for the Gini mean difference when the…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
Sufficient conditions for comparing the convolutions of heterogeneous gamma random variables in terms of the usual stochastic order are established. Such comparisons are characterized by the Schur convexity properties of the cumulative…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…
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…
We have investigated a weighted chi-square distribution of the variable $\xi$ which is a weighted sum of squared normally distributed independent variables whose weights are cosines of angles $\phi_k=2\pi k/N$, where $k \in \{0,1,...,N-1\}$…
In this note, we establish the convergence in distribution of the maxima of i.i.d. random variables to the Gumbel distribution with the associated normalizing sequences for several examples that are related to the normal distribution.…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…
We introduce a class of logarithmic Lambert W random variables for a specific family of distributions. In particular, we characterize the log-Lambert W random variables for chi-squared distributions which naturally appear in the likelihood…
A (p-1)-variate integral representation is given for the cumulative distribution function of the general p-variate non-central gamma distribution with a non-centrality matrix of any admissible rank. The real part of products of well known…
We provide in this paper simulation algorithms for one-sided and two-sided truncated normal distributions. These algorithms are then used to simulate multivariate normal variables with restricted parameter space for any covariance…
For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…
We address the asymptotic and approximate distributions of a large class of test statistics with quadratic forms used in association studies. The statistics of interest do not necessarily follow a chi-square distribution and take the…
In this paper we show that the conditional distribution of perturbed chi-quare risks can be approximated by certain distributions including the Gaussian ones. Our results are of interest for conditional extreme value models and multivariate…
We present four new mathematical methods, two exact and two approximate, along with open-source software, to compute the cdf, pdf and inverse cdf of the generalized chi-square distribution. Some methods are geared for speed, while others…
Several representations of the exact cdf of the sum of squares of n independent gamma-distributed random variables Xi are given, in particular by a series of gamma distribution functions. Using a characterization of the gamma distribution…
We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random…
This note provides the Stein equation for weighted sums of independent $\chi^{2}$ distributions.