Statistics and Probability African Society Editions

Chapter 6. On the Parameter Estimation by Method of Moments and Wald Type Test for Poisson Processes

Elhadji Ousseynou ACCRACHI, Ali Souleymane DABYE, and Alix Akwada GOUNOUNG

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Abstract

We consider two statistical problems for inhomogeneous Poisson processes. The first one concerns the parameter estimation and the second one is about the goodness of fit test. We develop the method of moments in parameter estimation problem and describe the asymptotic behavior of the new test based on the method of moments estimator. We show that the constructed estimators are consistent and asymptotically normal and for the test we find the limit distribution of the test statistics under hypothesis and show its consistency.

Chapter information

Source
Hamet Seydi, Gane Samb Lo, Aboubakary Diakhaby, eds., A Collection of Papers in Mathematics and Related Sciences, a Festschrift in Honour of the Late Galaye Dia, (Calgary, Alberta, 2018), 57-73

Dates
First available in Project Euclid: 26 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.spaseds/1569509466

Digital Object Identifier
doi:10.16929/sbs/2018.100-02-02

Subjects
Primary: 62F10: Point estimation 62F12: Asymptotic properties of estimators 62G10: Hypothesis testing 62G20: Asymptotic properties 62M05: Markov processes: estimation

Keywords
parameter estimation Poisson processes method of moments estimators consistency asymptotic normality test of Wald

Citation

ACCRACHI, Elhadji Ousseynou; DABYE, Ali Souleymane; GOUNOUNG, Alix Akwada. Chapter 6. On the Parameter Estimation by Method of Moments and Wald Type Test for Poisson Processes. A Collection of Papers in Mathematics and Related Sciences, 57--73, Statistics and Probability African Society, Calgary, Alberta, 2018. doi:10.16929/sbs/2018.100-02-02. https://projecteuclid.org/euclid.spaseds/1569509466


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