Question

How to calculate 95th percentile from mean and standard deviation of an exponential distribution?

Answer 1

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The qthqth quantile of a random variable XX is the value xx such that

Pr[X≤x]=q.Pr[X≤x]=q.So in your case q=0.25q=0.25, and0.25=Pr[X≤x]=FX(x)=1−e−x/β.0.25=Pr[X≤x]=FX(x)=1−e−x/β.This gives us e−x/4=0.75e−x/4=0.75, orx=−4log0.75≈1.15073.x=−4log⁡0.75≈1.15073.This assumes that the parametrization of the exponential distribution is by scale; i.e., if β=4β=4 this means E[X]=β=4E⁡[X]=β=4, rather than by rate--in which case E[X]=1/β=1/4E⁡[X]=1/β=1/4.