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Wallenius' Noncentral Hypergeometric Distribution: Probability Theory, Statistics, Hypergeometric Distribution, Sampling Bias, Urn Problem, Fisher's Noncentral Hypergeometric Distribution, Competition - Softcover

 
9786130322397: Wallenius' Noncentral Hypergeometric Distribution: Probability Theory, Statistics, Hypergeometric Distribution, Sampling Bias, Urn Problem, Fisher's Noncentral Hypergeometric Distribution, Competition

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory and statistics, Wallenius'' noncentral hypergeometric distribution is a generalization of the hypergeometric distribution where items are sampled with bias. This distribution can be illustrated as an urn model with bias. Assume, for example, that an urn contains m1 red balls and m2 white balls, totalling N = m1 + m2 balls. Each red ball has the weight ω1 and each white ball has the weight ω2. We will say that the odds ratio is ω = ω1 / ω2. Now we are taking n balls, one by one, in such a way that the probability of taking a particular ball at a particular draw is equal to its proportion of the total weight of all balls that lie in the urn at that moment. The number of red balls x1 that we get in this experiment is a random variable with Wallenius'' noncentral hypergeometric distribution.

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Reseña del editor

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory and statistics, Wallenius'' noncentral hypergeometric distribution is a generalization of the hypergeometric distribution where items are sampled with bias. This distribution can be illustrated as an urn model with bias. Assume, for example, that an urn contains m1 red balls and m2 white balls, totalling N = m1 + m2 balls. Each red ball has the weight ω1 and each white ball has the weight ω2. We will say that the odds ratio is ω = ω1 / ω2. Now we are taking n balls, one by one, in such a way that the probability of taking a particular ball at a particular draw is equal to its proportion of the total weight of all balls that lie in the urn at that moment. The number of red balls x1 that we get in this experiment is a random variable with Wallenius'' noncentral hypergeometric distribution.

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