Statistical properties of an estimator for the mean function of a compound cyclic Poisson process in the presence of linear trend | Zendy

Bonno Andri Wibowo | Zendy; I Wayan Mangku | Zendy; Siswadi Siswadi | Zendy

Open Access

Statistical properties of an estimator for the mean function of a compound cyclic Poisson process in the presence of linear trend

Author(s) -

Bonno Andri Wibowo,

I Wayan Mangku,

Siswadi Siswadi

Publication year - 2016

Publication title -

arab journal of mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.353

H-Index - 11

eISSN - 2588-9214

pISSN - 1319-5166

DOI - 10.1016/j.ajmsc.2016.08.004

Subject(s) - mathematics , estimator , poisson distribution , bounded function , function (biology) , compound poisson process , realization (probability) , interval (graph theory) , variance function , parametric statistics , statistics , mathematical analysis , poisson process , combinatorics , evolutionary biology , biology

The problem of estimating the mean function of a compound cyclic Poisson process with linear trend is considered. An estimator of this mean function is constructed and investigated. The cyclic component of intensity function of this process is not assumed to have any parametric form, but its period is assumed to be known. The slope of the linear trend is assumed to be positive, but its value is unknown. Moreover, we consider the case when there is only a single realization of the Poisson process is observed in a bounded interval. Asymptotic bias and variance of the proposed estimator are computed, when the size of interval indefinitely expands

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