Generalized Bernoulli process with long-range dependence and fractional binomial distribution

Generalized Bernoulli process with long-range dependence and fractional binomial distribution

Bernoulli process is a finite or infinite sequence of independent binary variables, Xi, i = 1, 2, · · ·, whose outcome is either 1 or 0 with probability P(Xi = 1) = p, P(Xi = 0) = 1 – p, for a fixed constant p ∈ (0, 1). We will relax the independence condition of Bernoulli variables, and develop a g...

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Autor principal: Lee Jeonghwa
Formato: article
Lenguaje:EN
Publicado: De Gruyter 2021
Materias:
bernoulli process
long-range dependence
hurst exponent
over-dispersed binomial model
60g10
60g22
Science (General)
Q1-390
Mathematics
QA1-939
Acceso en línea:https://doaj.org/article/80bcbe01796e43418a2f60b347a0c3ed
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spelling oai:doaj.org-article:80bcbe01796e43418a2f60b347a0c3ed2021-12-05T14:10:45ZGeneralized Bernoulli process with long-range dependence and fractional binomial distribution2300-229810.1515/demo-2021-0100https://doaj.org/article/80bcbe01796e43418a2f60b347a0c3ed2021-03-01T00:00:00Zhttps://doi.org/10.1515/demo-2021-0100https://doaj.org/toc/2300-2298Bernoulli process is a finite or infinite sequence of independent binary variables, Xi, i = 1, 2, · · ·, whose outcome is either 1 or 0 with probability P(Xi = 1) = p, P(Xi = 0) = 1 – p, for a fixed constant p ∈ (0, 1). We will relax the independence condition of Bernoulli variables, and develop a generalized Bernoulli process that is stationary and has auto-covariance function that obeys power law with exponent 2H – 2, H ∈ (0, 1). Generalized Bernoulli process encompasses various forms of binary sequence from an independent binary sequence to a binary sequence that has long-range dependence. Fractional binomial random variable is defined as the sum of n consecutive variables in a generalized Bernoulli process, of particular interest is when its variance is proportional to n2H, if H ∈ (1/2, 1).Lee JeonghwaDe Gruyterarticlebernoulli processlong-range dependencehurst exponentover-dispersed binomial model60g1060g22Science (General)Q1-390MathematicsQA1-939ENDependence Modeling, Vol 9, Iss 1, Pp 1-12 (2021)
institution DOAJ
collection DOAJ
language EN
topic bernoulli process
long-range dependence
hurst exponent
over-dispersed binomial model
60g10
60g22
Science (General)
Q1-390
Mathematics
QA1-939
spellingShingle bernoulli process
long-range dependence
hurst exponent
over-dispersed binomial model
60g10
60g22
Science (General)
Q1-390
Mathematics
QA1-939
Lee Jeonghwa
Generalized Bernoulli process with long-range dependence and fractional binomial distribution
description Bernoulli process is a finite or infinite sequence of independent binary variables, Xi, i = 1, 2, · · ·, whose outcome is either 1 or 0 with probability P(Xi = 1) = p, P(Xi = 0) = 1 – p, for a fixed constant p ∈ (0, 1). We will relax the independence condition of Bernoulli variables, and develop a generalized Bernoulli process that is stationary and has auto-covariance function that obeys power law with exponent 2H – 2, H ∈ (0, 1). Generalized Bernoulli process encompasses various forms of binary sequence from an independent binary sequence to a binary sequence that has long-range dependence. Fractional binomial random variable is defined as the sum of n consecutive variables in a generalized Bernoulli process, of particular interest is when its variance is proportional to n2H, if H ∈ (1/2, 1).
format article
author Lee Jeonghwa
author_facet Lee Jeonghwa
author_sort Lee Jeonghwa
title Generalized Bernoulli process with long-range dependence and fractional binomial distribution
title_short Generalized Bernoulli process with long-range dependence and fractional binomial distribution
title_full Generalized Bernoulli process with long-range dependence and fractional binomial distribution
title_fullStr Generalized Bernoulli process with long-range dependence and fractional binomial distribution
title_full_unstemmed Generalized Bernoulli process with long-range dependence and fractional binomial distribution
title_sort generalized bernoulli process with long-range dependence and fractional binomial distribution
publisher De Gruyter
publishDate 2021
url https://doaj.org/article/80bcbe01796e43418a2f60b347a0c3ed
work_keys_str_mv AT leejeonghwa generalizedbernoulliprocesswithlongrangedependenceandfractionalbinomialdistribution
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