Open AccessStrong Consistency and Asymptotic Distribution of Estimator for the Intensity Function Having Form of Periodic Function Multiplied by Power Function Trend of a Poisson Process
Author(s) -
Nina Valentika,
Wayan Mangku,
Windiani Erliana
Publication year - 2018
Publication title -
international journal of engineering and management research
Language(s) - English
Resource type - Journals
eISSN - 2394-6962
pISSN - 2250-0758
DOI - 10.31033/ijemr.v8i02.11652
Subject(s) - mathematics , estimator , asymptotic distribution , consistency (knowledge bases) , poisson distribution , function (biology) , kernel (algebra) , realization (probability) , mathematical analysis , statistics , combinatorics , discrete mathematics , evolutionary biology , biology
This manuscript discusses the strong consistency and the asymptotic distribution of an estimator for a periodic component of the intensity function having a form of periodic function multiplied by power function trend of a non-homogeneous Poisson process by using a uniform kernel function. It is assumed that the period of the periodic component of intensity function is known. An estimator for the periodic component using only a single realization of a Poisson process observed at a certain interval has been constructed. This estimator has been proved to be strongly consistent if the length of the observation interval indefinitely expands. Computer simulation also showed the asymptotic normality of this estimator.