Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T06:24:49.844Z Has data issue: false hasContentIssue false
  • English
  • Français

Partial orders and minimization of records in a sequence of independent random variables

Part of: Nonparametric inference

Published online by Cambridge University Press:  14 July 2016

Raúl Gouet  and
Jaime San Martín
Raúl Gouet*
Affiliation:
Universidad de Chile
Jaime San Martín*
Affiliation:
Universidad de Chile
*
∗Postal address: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170/3, Santiago, Chile.
∗Postal address: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170/3, Santiago, Chile.
Get access Rights & Permissions [Opens in a new window]

Abstract

Given independent random variables X1,…,Xn, with continuous distributions F1,…,Fn, we investigate the order in which these random variables should be arranged so as to minimize the number of upper records. We show that records are stochastically minimized if the sequence F1,…,Fn decreases with respect to a partial order, closely related to the monotone likelihood ratio property. Also, the expected number of records is shown to be minimal when the distributions are comparable in terms of a one-sided hazard rate ordering. Applications to parametric models are considered.

Keywords

Recordsorderings on distributions

MSC classification

Primary: 62G30: Order statistics; empirical distribution functions
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 4 , December 1999 , pp. 965 - 973
Copyright
Copyright © Applied Probability Trust 1999 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Partial funding provided by grants FONDECYT and FONDAP in Applied Mathematics.

References

Knuth, D. E. (1968). The Art of Computer Programming, Vol. 1, Fundamental Algorithms. Addison-Wesley, Reading, MA.Google Scholar
Nevzorov, V. B. (1988). Records. Theory Prob. Appl. 32, 201–228.CrossRefGoogle Scholar
Pfeifer, D. (1991). Some remarks on Nevzorov's record model. Adv. Appl. Prob. 23, 823–834.CrossRefGoogle Scholar
Shorrock, R. W. (1973). Record values and inter-record times. J. Appl. Prob. 10, 543–555.CrossRefGoogle Scholar
Stoyan, D. (1983). Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar