Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/266319 
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Erscheinungsjahr: 
2022
Quellenangabe: 
[Journal:] Statistics in Transition new series (SiTns) [ISSN:] 2450-0291 [Volume:] 23 [Issue:] 3 [Publisher:] Sciendo [Place:] Warsaw [Year:] 2022 [Pages:] 27-47
Verlag: 
Sciendo, Warsaw
Zusammenfassung: 
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.
Schlagwörter: 
Fibonacci probability distribution
generalized polynacci distribution
factorial moment generating function
method of moments
maximum likelihood estimator
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