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313557

Analytical Study for Periodic Functions and Estimation

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Last updated: 05 Jan 2025

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Abstract

In this article we consider a real process xTwhich is composed of a real function mT() and a white brownian noise UT. where the real function mT() represents a linear combination of known periodic functions ₁,….., k and some unknown parameters =(₁,...,k). We use the maximum likelihood method to estimate the unknown parameters. We proved a theorem which gives an upper bound for the probability that the absolute value of the Euclidian distance between the parameters and its estimators exceeds a small positive value ɛ. Some examples of periodic functions and the convergence of its sequence of means are given. Computation is performed for periodic functions i's of the form i(x)=sin ix. As application of periodic function we exposed MACHO project in the domain of astronomy.  

DOI

10.21608/esju.2005.313557

Keywords

White Brownian Noise - Time Series - Periodic Function, Periodicity, Periodogram - Maximum Likelihood Method - MACHO Project

Volume

49

Article Issue

1

Related Issue

42993

Issue Date

2005-06-01

Publish Date

2005-06-01

Page Start

74

Page End

92

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_313557.html

Detail API

https://esju.journals.ekb.eg/service?article_code=313557

Order

6

Type

Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

Analytical Study for Periodic Functions and Estimation

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Type

Article

Created At

28 Dec 2024