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Truncated normal distribution : ウィキペディア英語版 | Truncated normal distribution
In probability and statistics, the truncated normal distribution is the probability distribution of a normally distributed random variable whose value is either bounded below or above (or both). The truncated normal distribution has wide applications in statistics and econometrics. For example, it is used to model the probabilities of the binary outcomes in the probit model and to model censored data in the Tobit model. ==Definition==
Suppose has a normal distribution and lies within the interval . Then conditional on has a truncated normal distribution. Its probability density function, ƒ, for , is given by : and by ƒ=0 otherwise. Here, is the probability density function of the standard normal distribution and is its cumulative distribution function. There is an understanding that if , then , and similarly, if , then .
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