Truncated Normal Distribution - Definition

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

f(x;\mu,\sigma,a,b) = \frac{\frac{1}{\sigma}\phi(\frac{x - \mu}{\sigma})}{\Phi(\frac{b - \mu}{\sigma}) - \Phi(\frac{a - \mu}{\sigma}) }

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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