TECHNOLOGY OVERVIEW

Gamma Distribution

The BIS.Net Team BIS.Net Team

The gamma distribution is either a two parameter or three parameter family of continuous probability distributions.

Example of a Gamma Chart Example of a Gamma Distribution

Parameterization for the two-parameter family can be

  • With a shape parameter k and a scale parameter θ.
  • With a shape parameter α = k and an inverse scale parameter β = 1/θ, called a rate parameter.
  • With a shape parameter k and a mean parameter μ = kθ = α/β.

The probability density function for the two-parameter family with the second parametrization option above is

Gamma Formula

The three-parameter family has a location (offset) parameter delta to shift the location if there are negative values say.

This involves simply replacing x with say x-offset in the above pdf.

The gamma distribution has been used in cancer incidence studies, insurance and warranty claims, neuro science.

The BIS.NET Process Performance App uses sophisticated machine powered algorithms to obtain the parameters for the gamma distribution such that the Anderson Darling statistic is minimized.

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