Brazilian Journal of Probability and Statistics

Assigning probabilities to hypotheses in the context of a binomial distribution

Casper J. Albers, Otto J. W. F. Kardaun, and Willem Schaafsma

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Given is the outcome $s$ of $S\sim{\mathrm{B}}(n,p)$ ($n$ known, $p$ fully unknown) and two numbers $0<a\leq b<1$. Required are probabilities $\alpha_{<}(s)$, $\alpha_{a,b}(s)$, and $\alpha_{>}(s)$ of the hypotheses $\mathrm{H}_{<}$: $p<a$, $\mathrm{H}_{a,b}$: $a\leq p\leq b$, and $\mathrm{H}_{>}$: $p>b$, such that their sum is equal to 1. The degenerate case $a=b(=c)$ is of special interest. A method, optimal with respect to a class of functions, is derived under Neyman–Pearsonian restrictions, and applied to a case from medicine.

Article information

Braz. J. Probab. Stat., Volume 30, Number 1 (2016), 127-144.

Received: January 2013
Accepted: September 2014
First available in Project Euclid: 19 January 2016

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Zentralblatt MATH identifier

Hypothesis testing $p$-values $q$-values squared error loss weak unbiasedness


Albers, Casper J.; Kardaun, Otto J. W. F.; Schaafsma, Willem. Assigning probabilities to hypotheses in the context of a binomial distribution. Braz. J. Probab. Stat. 30 (2016), no. 1, 127--144. doi:10.1214/14-BJPS264.

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