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The graph of a probability mass function. All the values of this function must be non-negative and sum up to 1. In probability and statistics, a probability mass function (sometimes called probability function or frequency function [1]) is a function that gives the probability that a discrete random variable is exactly equal to some value. [2]
The probability mass function of a Poisson-distributed random variable with mean μ is given by (;) =!.for (and zero otherwise). The Skellam probability mass function for the difference of two independent counts = is the convolution of two Poisson distributions: (Skellam, 1946)
Besides the probability function, the cumulative distribution function, the probability mass function and the probability density function, the moment generating function and the characteristic function also serve to identify a probability distribution, as they uniquely determine an underlying cumulative distribution function. [10]
The reference [13] discusses techniques of evaluating the probability mass function of the Poisson binomial distribution. The following software implementations are based on it: The following software implementations are based on it:
The probability mass function (pmf) for the mass fraction of chains of length is: () = (). In this equation, k is the number of monomers in the chain, [1] and 0<a<1 is an empirically determined constant related to the fraction of unreacted monomer remaining. [2]
In statistics, especially in Bayesian statistics, the kernel of a probability density function (pdf) or probability mass function (pmf) is the form of the pdf or pmf in which any factors that are not functions of any of the variables in the domain are omitted. [1] Note that such factors may well be functions of the parameters of the
Probability mass function for Wallenius' Noncentral Hypergeometric Distribution for different values of the odds ratio ω. m 1 = 80, m 2 = 60, n = 100, ω = 0.1 ... 20. In probability theory and statistics, Wallenius' noncentral hypergeometric distribution (named after Kenneth Ted Wallenius) is a generalization of the hypergeometric distribution where items are sampled with bias.
In probability theory and statistics, the Van Houtum distribution is a discrete probability distribution named after prof. Geert-Jan van Houtum. [1] It can be characterized by saying that all values of a finite set of possible values are equally probable, except for the smallest and largest element of this set.
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