According the method of moments for sample (X1, X2,…,XN)

alpha = (M^2)/[M2 - M^2];

beta = [M2 - M^2]/M,

where M - sample mean, M=(Sigma Xi)/N; sample statistical Initial moment of the second order, M2=(Sigma Xi^2)/N.

It's pretty easy in R:

# Specify desired mode and sd of gamma distribution:

mode = 0.82

sd = 0.1

# Here are the corresponding rate and shape parameter values:

ra = ( mode + sqrt( mode^2 + 4*sd^2 ) ) / ( 2 * sd^2 )

sh = 1 + mode * ra

show(sh)

show(ra)

May be tried in fitting of gamma distribution by software by providing some known values.Gamma distribution may also tried by using the relationship of gamma to some simple distribution.

is there any software you recommend specifically 

According the method of moments for sample (X1, X2,…,XN)

alpha = (M^2)/[M2 - M^2];

beta = [M2 - M^2]/M,

where M - sample mean, M=(Sigma Xi)/N; sample statistical Initial moment of the second order, M2=(Sigma Xi^2)/N.

obtain the mean and variance of the data in study, develop a system of equations with the mean and variance.

mean = alpha * beta

variance = alpha * beta ^2

Dear Bibhuti,

I would definitely recommend R statistical software for which you can find a plenty of packages that are devoted to fitting different theoretical probability distributions including the method of L-moments (package 'lmomco') or the maximum likelihood estimation (package 'bbmle' wisely combined with some of the packages that include functions dealing with the Gamma's pdf or cdf - e.g. the package 'FAdist').

Note also that there are some other approaches to estimating the parameters of the Gamma distribution. For instance in section 4.4.3 of the following book:

Wilks, D.S., 2011. Statistical Methods in the Atmospheric Sciences. Academic Press, Oxford; Waltham, MA.

the author describes the method of ordinary moments and two approximations of maximum-likelihood estimates.

Hope this helps.

Best regards,

Ondrej

 Thanks Ondrej Ledvinka

Some helps may be obtained from SAS software in fitting of the gamma distribution.

alpha := Mean^2/Variance

beta  := Variance/Mean

Hi

You can find an online calculator for several distributions consist of Gamma on this website:

https://agrimetsoft.com/distributions-calculator/Gamma-Distribution-Fitting

Cheers

Who knows how to find the MLE of alpha in a gamma distribution

Using method of moments as for Gamma dist E(X)=alpha*beta and V(x) = alpha*beta^2. So get estimates of sample mean and variance of the data you believe follow Gamma dist and replace the sample mean and variance with E(X) and V(X) and solve the resulting equations to estimate alpha and beta of Gamma.

You can find fitting the 2-parameter (shape and scale) gamma distribution via

https://www.ncl.ucar.edu/Document/Functions/Built-in/dim_gamfit_n.shtml

in Python:

def gamm(x):

g1=sum(x)/len(x)

g2=sum([i**2 for i in x])/len(x)

alpha=g1**2/(g2-g1**2)

beta=(g2-g1**2)/g1

return alpha,beta

>>> a=[1, 3, 6, 5, 1, 1, 1, 8, 1, 1]

>>> gamm(a)

(1.2727272727272723, 2.2000000000000006)

There are 2 methods to calculate and fitting the parameters of statistical distributions; maximum likelihood and L-moment. As I mentioned above is via the "method of moments". But what Sohrab Kolsoumi recommended is "maximum likelihood ".