# Distributions with simple truncated expectations

by user180743   Last Updated October 10, 2019 03:19 AM

For a project I'm looking for continuous distributions which have a somewhat simple closed form for upper-truncation expectation ($$E[x|x>c]$$). Here are two examples I've found so far:

Exponential distribution ($$F(x)=1-e^{-\lambda x}$$): $$c+1/\lambda$$

Uniform distribution on $$(a,b)$$: $$\frac{c+b}{2}$$

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Assuming positive $$c$$:

The logistic distribution with mean 0, scale parameter $$s$$ has truncated expectation $$-ck + s(1+k)\log(1+k),\text{ where }k=e^{c/s}$$

The Laplace distribution with mean 0, scale parameter $$b$$ has truncated expectation $$(b+c)(1+e^{-c/b})/2$$

Matt F.
October 10, 2019 02:50 AM

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