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

[Marc Girondot]

Another situation for the presence of 0 is about dosage when 
concentration is below the detection limit. It is not necessary to 
discretize the data. We propose a method here:
Salvat-Leal I, Cortés-Gómez AA, Romero D, Girondot M (2022) New method 
for imputation of unquantifiable values using Bayesian statistics for a 
mixture of censored or truncated distributions: Application to trace 
elements measured in blood of olive ridley sea turtles from mexico. 
Animals 2022: 2919 doi 10.3390/ani12212919
with R code.
If the data has "true" 0, the gamma distribution is not the best choice 
as 0 is impossible with gamma distribution.

Marc

Le 19/01/2023 à 12:49, peter dalgaard a écrit :
> 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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