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  1. 1 Statistics in Transition new series

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  1. 1 Kwon Y.

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  1. 1 2022

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A comparison of the method of moments estimator and maximum likelihood estimator for the success probability in the Fibonacci-type probability distribution

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Kwon Y.
Statistics in Transition new series
|
2022
|
vol. 23
|
issue 3
27-41
EN
A Fibonacci-type probability distribution provides the probabilistic models for establishing stopping rules associated with the number of consecutive successes. It can be interpreted as a generalized version of a geometric distribution. In this article, after revisiting the Fibonaccitype probability distribution to explore its definition, moments and properties, we proposed numerical methods to obtain two estimators of the success probability: the method of moments estimator (MME) and maximum likelihood estimator (MLE). The ways both of them performed were compared in terms of the mean squared error. A numerical study demonsrated that the MLE tends to outperform the MME for most of the parameter space with various sample sizes.
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