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In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of successes (random draws for which the object drawn has a specified feature) in draws, without replacement, from a finite population of size that contains exactly objects with that feature, wherein each draw is either a success or a failure.
The Cauchy distribution, an example of a distribution which does not have an expected value or a variance. In physics it is usually called a Lorentzian profile , and is associated with many processes, including resonance energy distribution, impact and natural spectral line broadening and quadratic stark line broadening.
In probability theory and statistics, the negative hypergeometric distribution describes probabilities for when sampling from a finite population without replacement in which each sample can be classified into two mutually exclusive categories like Pass/Fail or Employed/Unemployed. As random selections are made from the population, each ...
The probability distribution of employed versus unemployed respondents in a sample of n respondents can be described as a noncentral hypergeometric distribution. The description of biased urn models is complicated by the fact that there is more than one noncentral hypergeometric distribution. Which distribution one gets depends on whether items ...
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p).
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.
The geometric distribution is the discrete probability distribution that describes when the first success in an infinite sequence of independent and identically distributed Bernoulli trials occurs. Its probability mass function depends on its parameterization and support.
The univariate noncentral hypergeometric distribution may be derived alternatively as a conditional distribution in the context of two binomially distributed random variables, for example when considering the response to a particular treatment in two different groups of patients participating in a clinical trial.