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So I have the following $CDF$ and I was wondering how will I be able to get the Maximum Likelihood Estimator since we do not have the $PDF$ to work with. The following $CDF$ is an exponential distribution that is "shifted" if you will by $L$ units where $x>L$ and $\lambda>0$.

\begin{align*} F(x) = 1 - e^{-\lambda(x - L)} \end{align*}

If it was a $PDF$, I realize that we should account for the $n$ observations, get the likelihood function, take the log and find the maximum via derivatives but we have the $CDF$ so that is not possible. Thanks so much for your help!

LearningIsPower
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1 Answers1

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The PDF can be calculated as the derivative of the CDF. Then you sound like you know what to do!

tristan
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