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GENERALIZATION OF THE PAIRWISE STOCHASTIC PRECEDENCE ORDER TO THE SEQUENCE OF RANDOM VARIABLES

Published online by Cambridge University Press:  18 March 2020

Maxim Finkelstein Open the ORCID record for Maxim Finkelstein [Opens in a new window]  and
Nil Kamal Hazra
Maxim Finkelstein
Affiliation:
Department of Mathematical Statistics and Actuarial Science, University of the Free State, 339 Bloemfontein 9300, South Africa; ITMO University, Saint Petersburg, Russia E-mail: [email protected]
Nil Kamal Hazra
Affiliation:
Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar 342037, India
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Abstract

We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence (SP) order that is defined for two random variables to the case n > 2. All conventional stochastic orders are transitive, whereas the SP order is not. Therefore, a new approach to compare the sequence of random variables had to be developed that resulted in the notion of the sequential precedence order. A sufficient condition for this order is derived and some examples are considered.

Keywords

hazard rate orderlikelihood ratio ordernontransitivitystochastic precedence orderusual stochastic order
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 699 - 707
Copyright
© Cambridge University Press 2020

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