Code for the Maximum likelihood esitmate for the gamma distribution , both parameters unknown
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In the book by [Klugmann: Loss Models] "HERE IS THE BOOK: BOOK" (pleasee see also the attachment Loss.jpg) [OR Here] on the page 383 I would like to see a command for Matlab that would compute the Maximum Likelihood Estimate
for the Gamma Distribution where both parameters α and θ are unknown , please see the attachment. I would like to see a command that would output for Example 15.4 these numbers:
=2561.1 and
=0.55616 for these data
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1289015/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1289020/image.png)
[27,82,115,126,155,161,243,294,340,384,457,680,855,877,974,1193,1340,1884,2558,15743]
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Torsten
il 8 Feb 2023
format long
data = [27,82,115,126,155,161,243,294,340,384,457,680,855,877,974,1193,1340,1884,2558,15743];
p = mle(data,'Distribution','Gamma')
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Torsten
il 9 Feb 2023
Modificato: Torsten
il 9 Feb 2023
sol = vpasolve([dlogfpdalpha==0,dlogfpdtheta==0],[alpha,theta],[0.5 1500])
gives theta more than 1500, namely 2561.14
Read in the documentation of "vpasolve" what the third argument given to the solver means.
Hint: It doesn't impose any constraint on the solution.
And you cannot impose any constraints on the solution.
You have a system of two equations in two unknowns. This is solved by
alpha: 0.55615779737149188594827727939715
theta: 2561.143629976936064991373664248
No way to influence these values in general.
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