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1 Statistics in Transition new series

1 2022

1 Kwon Y.

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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

100%

Kwon Y.

tom 23

nr 3

27-41

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.