Fitting Exponential Parameter via MLE

Basic Concepts

For the exponential distribution, the pdf is

exponential distribution pdf

and so the likelihood function for a data set {x1, …, xn} is

Likelihood function exponential distribution

Maximizing L(λ) is equivalent to maximizing the log-likelihood function LL(λ) = ln L(λ).

log-likelihood exponential distribution

It turns out that LL is maximized when λ = 1/, which is the same as the value that results from the method of moments (Distribution Fitting via Method of Moments). At this value, LL(λ) = n(ln λ – 1).

Reference

Wikipedia (2020) Exponential distribution
https://en.wikipedia.org/wiki/Exponential_distribution

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