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.

Answer 1

[Star Strider]

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

[Houda]

Thanks for the answer Star Strider, when I compared this result with the author table (paper of chang and fernander "On the source of aggregate fluctuations in emerging economies (2013)" page 1274, they report a gamma (2.060;0.0036) for the sigma a. how they get this result!!!!!

[Star Strider]

My pleasure.

I have absolutely no idea how they got that result. All I know is that with the data you posted and information I have on the gamma distribution, my calculations are correct.

I do not have access to that paper. There should be contact information for the authors. Write to them and ask.

[Houda]

Thanks a lot because I tried before to resolve this issue but with to not avail, thanks to you I found correct results as the autho, however, in many cases it was impossible. I attached the paper you can check by your self (table 2 P1274). take care.

[Star Strider]

My pleasure.

I will look through the paper.