TY - JOUR

T1 - Identification of parameters from the distribution of the maximum or minimum of Poisson random variables

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

UR - http://www.scopus.com/inward/record.url?scp=85115930015&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2021.109243

DO - 10.1016/j.spl.2021.109243

M3 - Article

AN - SCOPUS:85115930015

VL - 180

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

M1 - 109243

ER -