Gamma Distribution

Actuarial Path lesson on the gamma distribution.
We expand on the previous introductory lesson which motivated the gamma distribution via the Poisson counting process. Lots of details will be covered in this lesson!
The first one being application examples of the gamma distribution. That will give you a perspective of why we study the gamma distribution. What practical uses and implementations it has in various application fields.
Secondly, we will introduce the gamma function, and show how it relates to the factorial function.
We use the gamma function to derive the standard gamma distribution function. We then extend the standard gamma distribution by scaling it by a constant. That will give us what we call the two-parameter gamma distribution. We show its probability density function, derive its moment generating function, its mean and its variance.
We finally show how the gamma distribution relates to the exponential distribution. That is, we show that the exponential distribution is a special case of the gamma distribution. Lesson given by Bereket Kindo

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[@StatCourses]

I’ll see if I can find it. It’s been a while since I created this video.