On estimating the parameter of a truncated geometric distribution

Thomasson, R. L.; Kapadia, C. H.

doi:10.1007/bf02911664

Cited by 10 publications

(10 citation statements)

References 2 publications

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“…Maximum likelihood estimation for the truncated geometric model is known since Thomasson and Kapadia [16]. Consider the stationary probability distribution given by (1).…”

Section: Maximum Likelihood Estimatormentioning

confidence: 99%

Traffic Intensity Estimation in Finite Markovian Queueing Systems

Cruz

Almeida

D’Angelo

et al. 2018

Mathematical Problems in Engineering

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In many everyday situations in which a queue is formed, queueing models may play a key role. By using such models, which are idealizations of reality, accurate performance measures can be determined, such as traffic intensity ( ), which is defined as the ratio between the arrival rate and the service rate. An intermediate step in the process includes the statistical estimation of the parameters of the proper model. In this study, we are interested in investigating the finite-sample behavior of some well-known methods for the estimation of for single-server finite Markovian queues or, in Kendall notation, / /1/ queues, namely, the maximum likelihood estimator, Bayesian methods, and bootstrap corrections. We performed extensive simulations to verify the quality of the estimators for samples up to 200. The computational results show that accurate estimates in terms of the lowest mean squared errors can be obtained for a broad range of values in the parametric space by using the Jeffreys' prior. A numerical example is analyzed in detail, the limitations of the results are discussed, and notable topics to be further developed in this research area are presented.

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“…Maximum likelihood estimation for the truncated geometric model is known since Thomasson and Kapadia [16]. Consider the stationary probability distribution given by (1).…”

Section: Maximum Likelihood Estimatormentioning

confidence: 99%

Traffic Intensity Estimation in Finite Markovian Queueing Systems

Cruz

Almeida

D’Angelo

et al. 2018

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…The desired efficiency is given by the ratio of equation (3.1) of the authors [4] to equation (3.2). The equations for the asymptotic variances are too complicated to permit any analytic conclusions.…”

Section: E (T') _ Q+l E (To') P ' E (T[) Pmentioning

confidence: 99%

“…If the random variable Y is as defined by the authors [4], the probability mass function of Y is This equation is identical to equation (2.1) given by the authors [4] which was used in constructing Table 1 [4]. Therefore, the method of moment estimator is identical to the maximum likelihood estimator.…”

Section: Introductionmentioning

confidence: 97%

“…Before describing Rider's modified method of moments, it will be shown first that the usual method of moments estimator is identical to the maximum likelihood estimator [4]. If the random variable Y is as defined by the authors [4], the probability mass function of Y is This equation is identical to equation (2.1) given by the authors [4] which was used in constructing Table 1 [4].…”

Section: Introductionmentioning

confidence: 98%

“…This is derived by a modified method of moments procedure suggested for use with truncated distributions by Rider [2], [3] and compare its efficiency relative to the maximum likelihood estimator given by the authors [4]. The advantage of this method, as compared to maximum likelihood, is that it yields an explicit solution for the estimator, so that the computation of the estimator does not require the solution of a high-degree polynomial.…”

Section: Introductionmentioning

confidence: 98%

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