CODEWITHSUNDEEP
r
lina bina
lina bina

Reputation: 1

Maximum likelihood of Compound Poisson Distributions

I'm trying to compute a maximum likelihood of the compound Poisson-Gamma distribution in R. The distribution is defined by $ \sum_{j=1}^{N} Y_j $ where $Y_n$ is i.i.d sequence independent $gamma(k,\theta)$ values and $N$ is a Poisson distribution with parameter $\beta$. I'm trying to estimate the parameters $\theta$ and $\beta$ without luck.

Upvotes: 0

Views: 428

Answers (1)

Stefanos
Stefanos

Reputation: 929

If you wanted to do something similar, but for a negative binomial distribution, then you can use the the function negbin.mle from the package Rfast

y <- rpois(100, 2)

Rfast::negbin.mle(y)

Output

$iters
[1] 5

$loglik
[1] -162.855

$param
success probability  number of failures                mean 
          0.9963271         480.1317031           1.7700000

Also if you run the command:

Rfast::negbin.mle

You can see what the function is computing.

You can also check the functions manual with:

?Rfast::negbin.mle

Edit:

Unfortunately I haven't found something that perfectly fits your answer. As Ben states, this answer is for a Poisson with Gamma-distributed mean.

Upvotes: 1

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