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Zero-inflated model : ウィキペディア英語版
Zero-inflated model
In statistics, a zero-inflated model is a statistical model based on a zero-inflated probability distribution, i.e. a distribution that allows for frequent zero-valued observations.
==Zero-inflated Poisson==
The first zero-inflated model is zero-inflated Poisson model. The zero-inflated Poisson model concerns a random event containing excess zero-count data in unit time. For example, the number of insurance claims within a population for a certain type of risk would be zero-inflated by those people who have not taken out insurance against the risk and thus are unable to claim. The zero-inflated Poisson (ZIP) model employs two components that correspond to two zero generating processes. The first process is governed by a binary distribution that generates structural zeros. The second process is governed by a Poisson distribution that generates counts, some of which may be zero. The two model components are described as follows:
: \Pr (y_j = 0) = \pi + (1 - \pi) e^
:\Pr (y_j = h_i) = (1 - \pi) \frac} ,\qquad h_i \ge 1
where the outcome variable y_j has any non-negative integer value, \lambda_i is the expected Poisson count for the ith individual; \pi is the probability of extra zeros.
The mean is (1-\pi) \lambda and the variance is \lambda (1-\pi) (1+\lambda \pi) .

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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