Houda asked . 2022-05-04

How to define the bounds of Gamma distribution (a,b)

Hey everybody,

I am looking for how to calculate the interval of the gamma density distribution when setting the priors in Bayesian estimation. For beta(a,b) the mean of X= E(X)=a/(a+b) and variance is V(X)=(a+b)/(a+b+1)(a+b)^2, as we define the mean and varaince from the common values in the literature I return and calculate a and b. Please for gamma (a,b) distribution with E(X)=0.74 and std(X)=0.0056 how to find a and b?

Many thanks in advance.

bayesian distribution , AI, Data Science, and Statistics , Statistics and Machine Learning Toolbox

Expert Answer

John Williams answered . 2024-12-21 00:31:55

The Wikipedia article on the Gamma distribution (link) indicates that:

gamma_mean = a*b;
gamma_var = a*b^2;

so with your data:

gamma_mean = 0.74
gamma_var = 0.0056^2                        % Var is StDev^2
b = gamma_var/gamma_mean
a = gamma_mean/b

b =
   4.2378e-05

a =
        17462

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