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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.
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 ...
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 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 ...
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.
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one.
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.
The product of independent random variables X and Y may belong to the same family of distribution as X and Y: Bernoulli distribution and log-normal distribution. Example: If X 1 and X 2 are independent log-normal random variables with parameters (μ 1, σ 2 1) and (μ 2, σ 2 2) respectively, then X 1 X 2 is a log-normal random variable with ...