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The Birnbaum–Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. The chi distribution. The noncentral chi distribution; The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables.
A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
The probability mass function for the binomial distribution is: (=) = () where is the probability of getting successes in trials, and () is the binomial coefficient. For this computation, p {\displaystyle p} is the probability that a person qualified for board service is female, k {\displaystyle k} is the number of female board members, and n ...
For any random variable whose probability distribution function belongs to such a family, the distribution function of = + also belongs to the family (where = means "equal in distribution"—that is, "has the same distribution as"). In other words, a class of probability distributions is a location–scale family if for all cumulative ...
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein each of some finite whole number n of outcome values are equally likely to be observed. Thus every one of the n outcome values has equal probability 1/n. Intuitively, a discrete uniform distribution is "a known, finite number ...
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
The posterior distribution in general describes the parameter in question, and in this case the parameter itself is a discrete probability distribution, i.e. the actual categorical distribution that generated the data. For example, if 3 categories in the ratio 40:5:55 are in the observed data, then ignoring the effect of the prior distribution ...
The distribution of words ranked by their frequency in a random text corpus is approximated by a power-law distribution, known as Zipf's law.. If one plots the frequency rank of words contained in a moderately sized corpus of text data versus the number of occurrences or actual frequencies, one obtains a power-law distribution, with exponent close to one (but see Powers, 1998 and Gelbukh ...