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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
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]
It is equivalent to, and sometimes called, the z-transform of the probability mass function. Other generating functions of random variables include the moment-generating function, the characteristic function and the cumulant generating function.
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)
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In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion = + + +.
In probability theory and statistics, the zeta distribution is a discrete probability distribution.If X is a zeta-distributed random variable with parameter s, then the probability that X takes the positive integer value k is given by the probability mass function
The probability mass function is therefore sometimes referred to as the discrete density function. In both cases, the cumulative distribution function is the integral (or, in the discrete case, the sum) for all values less than or equal to the current value of x , and so shows the accumulated probability so far.