[R] MLE Estimation of Gamma Distribution Parameters for data with 'zeros'

[peter dalgaard]

Not necessarily homework, Bert. There's a generic issue with MLE and rounded data, in that gamma densities may be 0 at the boundary but small numbers are represented as 0, making the log-likelihood -Inf. 

The cleanest way out is to switch to a discretized distribution in the likelihood, so that instead of log(dgamma(0,...)) you use log(pgamma(.005,..) - pgamma(0,...)) == pgamma(.005,..., log=TRUE). (For data rounded to nearest .01, that is). Cruder techniques would be to just add, like, .0025 to all the zeros. 

-pd

> On 10 Jan 2023, at 18:42 , Bert Gunter <bgunter.4567 using gmail.com> wrote:
> 
> Is this homework? This list has a no-homework policy.
> 
> 
> -- Bert
> 
> On Tue, Jan 10, 2023 at 8:13 AM Nyasha <kahuninyasha13296 using gmail.com> wrote:
>> 
>> Please how can one go about this one? I don't know how to go about it.
>> 
>>        [[alternative HTML version deleted]]
>> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
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