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

Kwon Yeil ()
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Kwon Yeil: University of Central Arkansas, USA .

Statistics in Transition New Series, 2022, vol. 23, issue 3, 27-47

Abstract: 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 Fibonacci-type 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 demon-srated that the MLE tends to outperform the MME for most of the parameter space with various sample sizes.

Keywords: Fibonacci probability distribution; generalized polynacci distribution; factorial moment generating function; method of moments; maximum likelihood estimator (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:stintr:v:23:y:2022:i:3:p:27-47:n:3

DOI: 10.2478/stattrans-2022-0028

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