Abstract
This present work aims to propose an estimator in order to estimate the probability of success of a binomial model that incorporates the extrabinomial variation generated by zero-inflated samples. The construction of this estimator was carried out with a theoretical basis given by the Holder function and its performance was evaluated through Monte Carlo simulation considering different sample sizes, parametric values (π), and excess of zero proportions (γ). It was concluded that for the situations in (γ = 0.20) and (γ = 0.50) that the proposed estimator presents promising results based on the specified margin of error.
Highlights
IntroductionThe inference on the parameter of a binomial population proportion, in general, is carried out considering sampling units are independent and provenient from a single population
Augusto Maciel da Silva & Marcelo Angelo CirilloThe inference on the parameter of a binomial population proportion, in general, is carried out considering sampling units are independent and provenient from a single population.there are situations in certain data sets where the sampling variance may be superior in relation to the expected variability in the binomial model
Some recommendations made by Ruckstuhl & Welsh (2001) were mentioned, in a way that, when assuming c1 = 0 and c2 → ∞, πwill correspond to the minimum relative entropy estimator which is identical to the maximum likelihood estimator (MLE) of the binomial model
Summary
The inference on the parameter of a binomial population proportion, in general, is carried out considering sampling units are independent and provenient from a single population. Some recommendations made by Ruckstuhl & Welsh (2001) were mentioned, in a way that, when assuming c1 = 0 and c2 → ∞, πwill correspond to the minimum relative entropy estimator which is identical to the maximum likelihood estimator (MLE) of the binomial model. As a result of the above motivation, the present work aims to construct a new estimator in order to estimate the probability of success of a binomial distribution given a zero-inflated sample. We understand that a problem of a continuous nature that is treated in a discretized way, depending on the algorithm to be used, or even, in an application with real data may occasionally cause a non-fitted estimate With of a modification in (3), in such manner that the researcher may fix an only value for the constants c1 and c2, based on a single point represented by the maximum likelihood estimator and not on every point of the parametric dominium, as suggested in (4)
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