ESTIMATING THE INTENSITY IN THE FORM OF A POWER FUNCTION OF AN INHOMOGENEOUS POISSON PROCESS | Zendy

I Wayan Mangku | Zendy; I. WIDIYASTUTI | Zendy; I Gusti Putu Purnaba | Zendy

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ESTIMATING THE INTENSITY IN THE FORM OF A POWER FUNCTION OF AN INHOMOGENEOUS POISSON PROCESS

Author(s) -

I Wayan Mangku,

I. WIDIYASTUTI,

I Gusti Putu Purnaba

Publication year - 2005

Publication title -

milang journal of mathematics and its applications

Language(s) - English

Resource type - Journals

ISSN - 2963-5233

DOI - 10.29244/jmap.4.1.51-57

Subject(s) - estimator , mathematics , poisson distribution , compound poisson process , bounded function , minimum variance unbiased estimator , function (biology) , realization (probability) , asymptotic distribution , delta method , poisson process , statistics , mathematical analysis , evolutionary biology , biology

An estimator of the intensity in the form of a power function of an inhomogeneous Poisson process is constructed and investigated. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias, variance and the mean- squared error of the proposed estimator are computed. Asymptotic normality of the estimator is also established.

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