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 -