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

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