Comparisons of order statistics from heterogeneous negative binomial variables with applications

Jianbin Chen; Yiying Zhang; Peng Zhao

doi:10.1080/02331888.2019.1580281

Comparisons of order statistics from heterogeneous negative binomial variables with applications

Jianbin Chen, Yiying Zhang^*, Peng Zhao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

This paper studies the ordering properties of extreme order statistics arising from independent negative binomial random variables. Employing the useful tool of majorization-type orders, sufficient conditions are given for comparing extreme negative binomial order statistics according to the usual stochastic order. Some numerical examples are provided to illustrate the theoretical results. Applications in Poisson-Gamma shock model in reliability engineering and claim frequency in insurance are presented to show the practicability of our results as well.

Original language	English
Pages (from-to)	990-1011
Number of pages	22
Journal	Statistics
Volume	53
Issue number	5
DOIs	https://doi.org/10.1080/02331888.2019.1580281
Publication status	Published - 3 Sept 2019
Externally published	Yes

Keywords

60K10
Order statistics
Primary 90B25
Secondary 60E15
majorization order
negative binomial distribution
p-larger order
usual stochastic order

Access to Document

10.1080/02331888.2019.1580281

Cite this

@article{16bf95f2bf704a44b0271180ddf60608,

title = "Comparisons of order statistics from heterogeneous negative binomial variables with applications",

abstract = "This paper studies the ordering properties of extreme order statistics arising from independent negative binomial random variables. Employing the useful tool of majorization-type orders, sufficient conditions are given for comparing extreme negative binomial order statistics according to the usual stochastic order. Some numerical examples are provided to illustrate the theoretical results. Applications in Poisson-Gamma shock model in reliability engineering and claim frequency in insurance are presented to show the practicability of our results as well.",

keywords = "60K10, Order statistics, Primary 90B25, Secondary 60E15, majorization order, negative binomial distribution, p-larger order, usual stochastic order",

author = "Jianbin Chen and Yiying Zhang and Peng Zhao",

note = "Publisher Copyright: {\textcopyright} 2019, {\textcopyright} 2019 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2019",

month = sep,

day = "3",

doi = "10.1080/02331888.2019.1580281",

language = "English",

volume = "53",

pages = "990--1011",

journal = "Statistics",

issn = "0233-1888",

publisher = "Taylor and Francis Ltd.",

number = "5",

}

TY - JOUR

T1 - Comparisons of order statistics from heterogeneous negative binomial variables with applications

AU - Chen, Jianbin

AU - Zhang, Yiying

AU - Zhao, Peng

PY - 2019/9/3

Y1 - 2019/9/3

N2 - This paper studies the ordering properties of extreme order statistics arising from independent negative binomial random variables. Employing the useful tool of majorization-type orders, sufficient conditions are given for comparing extreme negative binomial order statistics according to the usual stochastic order. Some numerical examples are provided to illustrate the theoretical results. Applications in Poisson-Gamma shock model in reliability engineering and claim frequency in insurance are presented to show the practicability of our results as well.

AB - This paper studies the ordering properties of extreme order statistics arising from independent negative binomial random variables. Employing the useful tool of majorization-type orders, sufficient conditions are given for comparing extreme negative binomial order statistics according to the usual stochastic order. Some numerical examples are provided to illustrate the theoretical results. Applications in Poisson-Gamma shock model in reliability engineering and claim frequency in insurance are presented to show the practicability of our results as well.

KW - 60K10

KW - Order statistics

KW - Primary 90B25

KW - Secondary 60E15

KW - majorization order

KW - negative binomial distribution

KW - p-larger order

KW - usual stochastic order

UR - https://www.scopus.com/pages/publications/85070206305

U2 - 10.1080/02331888.2019.1580281

DO - 10.1080/02331888.2019.1580281

M3 - Article

AN - SCOPUS:85070206305

SN - 0233-1888

VL - 53

SP - 990

EP - 1011

JO - Statistics

JF - Statistics

IS - 5

ER -

Comparisons of order statistics from heterogeneous negative binomial variables with applications

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this