Abstract
Let X1,X2,..., be a sequence of independent and identically distributed random variables with absolutely continuous distribution function F. For n ≥ 1, we denote the order statistics of X1,X2,...,Xn by X1,n ≤ ... Xn,n. Define L(1) = 1, L(n+1) = min{j: j > L(n), Xj > Xj-1,j-1}, and X(n) = XL(n),L(n), n ≥ 1. The sequence {X(n)} ({L(n)}) is called upper record statistics (times). In this article, we deal with unimodality of record statistics. We also deal with the strong unimodality of record statistics.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 395-398 |
| Number of pages | 4 |
| Journal | Statistics and Probability Letters |
| Volume | 56 |
| Issue number | 4 |
| DOIs | |
| State | Published - Feb 15 2002 |
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All Science Journal Classification (ASJC) codes
- Statistics, Probability and Uncertainty
- Statistics and Probability
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Unimodality of the distribution of record statistics. / Basak, Prasanta; Basak, Indrani.
In: Statistics and Probability Letters, Vol. 56, No. 4, 15.02.2002, p. 395-398.Research output: Contribution to journal › Article
TY - JOUR
T1 - Unimodality of the distribution of record statistics
AU - Basak, Prasanta
AU - Basak, Indrani
PY - 2002/2/15
Y1 - 2002/2/15
N2 - Let X1,X2,..., be a sequence of independent and identically distributed random variables with absolutely continuous distribution function F. For n ≥ 1, we denote the order statistics of X1,X2,...,Xn by X1,n ≤ ... Xn,n. Define L(1) = 1, L(n+1) = min{j: j > L(n), Xj > Xj-1,j-1}, and X(n) = XL(n),L(n), n ≥ 1. The sequence {X(n)} ({L(n)}) is called upper record statistics (times). In this article, we deal with unimodality of record statistics. We also deal with the strong unimodality of record statistics.
AB - Let X1,X2,..., be a sequence of independent and identically distributed random variables with absolutely continuous distribution function F. For n ≥ 1, we denote the order statistics of X1,X2,...,Xn by X1,n ≤ ... Xn,n. Define L(1) = 1, L(n+1) = min{j: j > L(n), Xj > Xj-1,j-1}, and X(n) = XL(n),L(n), n ≥ 1. The sequence {X(n)} ({L(n)}) is called upper record statistics (times). In this article, we deal with unimodality of record statistics. We also deal with the strong unimodality of record statistics.
UR - http://www.scopus.com/inward/record.url?scp=0037082550&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037082550&partnerID=8YFLogxK
U2 - 10.1016/S0167-7152(02)00028-7
DO - 10.1016/S0167-7152(02)00028-7
M3 - Article
AN - SCOPUS:0037082550
VL - 56
SP - 395
EP - 398
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
SN - 0167-7152
IS - 4
ER -