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



Answers 1


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.
Matt F.
October 10, 2019 02:50 AM

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