The Annals of Statistics

Monotonicity in the Noncentrality Parameter of the Ratio of Two Noncentral $t$-Densities

Robert A. Wijsman

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Abstract

Let $p_\nu(t, \delta)$ be the density at $t$ of a noncentral $t$-variable with $\nu$ degrees of freedom and noncentrality parameter $\delta$. It is proved that for any $d > 0$ and fixed $t, p_\nu(t, \delta + d)/p_\nu(t, \delta)$ is a strictly decreasing function of $\delta$.

Article information

Source
Ann. Statist., Volume 11, Number 3 (1983), 1008-1010.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346269

Digital Object Identifier
doi:10.1214/aos/1176346269

Mathematical Reviews number (MathSciNet)
MR707953

Zentralblatt MATH identifier
0515.62025

JSTOR
links.jstor.org

Subjects
Primary: 62E99: None of the above, but in this section
Secondary: 62L10: Sequential analysis 33A65

Keywords
Noncentral $t$ density ratio monotonicity noncentrality parameter

Citation

Wijsman, Robert A. Monotonicity in the Noncentrality Parameter of the Ratio of Two Noncentral $t$-Densities. Ann. Statist. 11 (1983), no. 3, 1008--1010. doi:10.1214/aos/1176346269. https://projecteuclid.org/euclid.aos/1176346269


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