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Zero-truncated Poisson distribution : ウィキペディア英語版
Zero-truncated Poisson distribution

In probability theory, the zero-truncated Poisson (ZTP) distribution is a certain discrete probability distribution whose support is the set of positive integers. This distribution is also known as the conditional Poisson distribution or the positive Poisson distribution. It is the conditional probability distribution of a Poisson-distributed random variable, given that the value of the random variable is not zero. Thus it is impossible for a ZTP random variable to be zero. Consider for example the random variable of the number of items in a shopper's basket at a supermarket checkout line. Presumably a shopper does not stand in line with nothing to buy (i.e. the minimum purchase is 1 item), so this phenomenon may follow a ZTP distribution.〔
(【引用サイトリンク】title=Stata Data Analysis Examples: Zero-Truncated Poisson Regression )
Since the ZTP is a truncated distribution with the truncation stipulated as , one can derive the probability mass function from a standard Poisson distribution ) as follows:

: g(k;\lambda) = P(X = k \mid k > 0) =
\frac =
\frac = \frac
The mean is
: \operatorname()=\frac
and the variance is
: \operatorname()=\frac} =
\frac\left()
==References==


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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