Identification of parameters from the distribution of the maximum or minimum of Poisson random variables

Bara Kim; Jeongsim Kim

doi:10.1016/j.spl.2021.109243

Identification of parameters from the distribution of the maximum or minimum of Poisson random variables

Bara Kim, Jeongsim Kim

Department of Mathematics

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

Abstract

Bi and Mukherjea (2011) considered the following problem: If X₁,…,X_n are independent Poisson distributed random variables with parameters λ₁,…,λ_n, respectively, then does the distribution of max{X₁,…,X_n} or of min{X₁,…,X_n} uniquely determine the parameters? They proved that the distribution of max{X₁,X₂,X₃} uniquely determines λ₁,λ₂ and λ₃. In this paper, we prove the identifiability problem of parameters from the distribution of max{X₁,…,X_n} or of min{X₁,…,X_n} for any value of n.

Original language	English
Article number	109243
Journal	Statistics and Probability Letters
Volume	180
DOIs	https://doi.org/10.1016/j.spl.2021.109243
Publication status	Published - 2022 Jan

Bibliographical note

Funding Information:
We are grateful to the reviewers for their valuable comments and suggestions. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2B5B01001864 ). J. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568 ).

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Distribution of maximum
Distribution of minimum
Identification of parameters
Poisson distributions

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2021.109243

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title = "Identification of parameters from the distribution of the maximum or minimum of Poisson random variables",

abstract = "Bi and Mukherjea (2011) considered the following problem: If X1,…,Xn are independent Poisson distributed random variables with parameters λ1,…,λn, respectively, then does the distribution of max{X1,…,Xn} or of min{X1,…,Xn} uniquely determine the parameters? They proved that the distribution of max{X1,X2,X3} uniquely determines λ1,λ2 and λ3. In this paper, we prove the identifiability problem of parameters from the distribution of max{X1,…,Xn} or of min{X1,…,Xn} for any value of n.",

keywords = "Distribution of maximum, Distribution of minimum, Identification of parameters, Poisson distributions",

author = "Bara Kim and Jeongsim Kim",

note = "Funding Information: We are grateful to the reviewers for their valuable comments and suggestions. B. Kim{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2B5B01001864 ). J. Kim{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568 ). Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2022",

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doi = "10.1016/j.spl.2021.109243",

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AU - Kim, Bara

AU - Kim, Jeongsim

N1 - Funding Information: We are grateful to the reviewers for their valuable comments and suggestions. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2B5B01001864 ). J. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568 ). Publisher Copyright: © 2021 Elsevier B.V.

PY - 2022/1

Y1 - 2022/1

N2 - Bi and Mukherjea (2011) considered the following problem: If X1,…,Xn are independent Poisson distributed random variables with parameters λ1,…,λn, respectively, then does the distribution of max{X1,…,Xn} or of min{X1,…,Xn} uniquely determine the parameters? They proved that the distribution of max{X1,X2,X3} uniquely determines λ1,λ2 and λ3. In this paper, we prove the identifiability problem of parameters from the distribution of max{X1,…,Xn} or of min{X1,…,Xn} for any value of n.

AB - Bi and Mukherjea (2011) considered the following problem: If X1,…,Xn are independent Poisson distributed random variables with parameters λ1,…,λn, respectively, then does the distribution of max{X1,…,Xn} or of min{X1,…,Xn} uniquely determine the parameters? They proved that the distribution of max{X1,X2,X3} uniquely determines λ1,λ2 and λ3. In this paper, we prove the identifiability problem of parameters from the distribution of max{X1,…,Xn} or of min{X1,…,Xn} for any value of n.

KW - Distribution of maximum

KW - Distribution of minimum

KW - Identification of parameters

KW - Poisson distributions

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DO - 10.1016/j.spl.2021.109243

M3 - Article

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SN - 0167-7152

VL - 180

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 109243

ER -

Identification of parameters from the distribution of the maximum or minimum of Poisson random variables

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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