On the restrictiveness of the usual stochastic order and the likelihood ratio order

Sela Fried

doi:10.1016/j.spl.2020.109012

On the restrictiveness of the usual stochastic order and the likelihood ratio order

Sela Fried

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Every element θ=(θ₁,…,θ_n) of the probability n-simplex induces a probability distribution P_θ of a random variable X that can assume only a finite number of real values x₁<⋯<x_n by defining P_θ(X=x_i)=θ_i,1≤i≤n. We show that if Θ and Θ^′ are two random vectors uniformly distributed on Δⁿ, then [Formula presented] and [Formula presented], where ≤_st and ≤_lr denote the usual stochastic order and the likelihood ratio order, respectively.

Original language	English
Article number	109012
Journal	Statistics and Probability Letters
Volume	170
DOIs	https://doi.org/10.1016/j.spl.2020.109012
State	Published - 1 Mar 2021

Keywords

Probability
Simplex
Stochastic orders

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2020.109012

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abstract = "Every element θ=(θ1,…,θn) of the probability n-simplex induces a probability distribution Pθ of a random variable X that can assume only a finite number of real values x1<⋯n by defining Pθ(X=xi)=θi,1≤i≤n. We show that if Θ and Θ′ are two random vectors uniformly distributed on Δn, then [Formula presented] and [Formula presented], where ≤st and ≤lr denote the usual stochastic order and the likelihood ratio order, respectively.",

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AB - Every element θ=(θ1,…,θn) of the probability n-simplex induces a probability distribution Pθ of a random variable X that can assume only a finite number of real values x1<⋯n by defining Pθ(X=xi)=θi,1≤i≤n. We show that if Θ and Θ′ are two random vectors uniformly distributed on Δn, then [Formula presented] and [Formula presented], where ≤st and ≤lr denote the usual stochastic order and the likelihood ratio order, respectively.

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KW - Simplex

KW - Stochastic orders

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JO - Statistics and Probability Letters

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ER -

On the restrictiveness of the usual stochastic order and the likelihood ratio order

Abstract

Keywords

ASJC Scopus subject areas

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