Jtourkis

Gamma distribution

I believe an edit is needed to the Gamma distribution page. In the Method of Moments text box at the top of the page, please add theta = V[X]/E[X] & k = E[X]^2/V[X].

Information to be added or removed: theta = V[X]/E[X] (added); k = E[X]^2/V[X]

Explanation of issue: If you calculate k and theta using the mean and variance stated, you can get the following method of moments estimators for theta and k.

References supporting change: Solve the system of equations:

Mean = k * theta => k = mean/theta

Replace k in terms of theta:

Variance = k*theta^2 => Variance = (mean/theta)*theta^2 = mean * theta => theta = variance / mean => theta = V[X]/E[X]

Then solve mean equation for k replacing theta with variance/mean.

Mean= k*(Variance/Mean)=> k= Mean/(Variance/Mean) => k = Mean^2/Variance => k = E[X]^2/V[X]

James Tourkistas

 Not done: this is the talk page for communicating with the user Jtourkis (talk · contribs). Please make your request at the talk page for the article concerned. JTP ^{(talk • contribs)} 21:14, 12 August 2020 (UTC)

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