Gamma distribution — Time to ‘r’th arrival

In lesson 45, Joe and Devine meet again, for the eighth time, to discuss Gamma distribution.

Joe summarizes how to derive the probability density function for the exponential distribution. He identifies that it is the continuous analog of the Geometric distribution.

Being a curious kid, he asks the right question.

Does the exponential distribution also have a related distribution that measures the wait time till the ‘r’th arrival?

Devine says that there is a related distribution that can be used to estimate the time to the ‘r’th arrival. It is called the Gamma distribution.

They both discuss how to derive the probability density function for the Gamma distribution using convolution.

The Gamma distribution has two control parameters, the the scale parameter (lambda) and the shape parameter (r).

Gamma distribution is frequently used to fit data with significant skewness such as the rainfall and insurance claims data.

Read the full lesson here.

Lesson 45 – Time to ‘r’th arrival: The language of Gamma distribution

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