English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider the problem of comparing two Poisson parameters from the Bayesianperspective. Kawasaki and Miyaoka (2012b) proposed the Bayesian index$P(\lambda_1 < \lambda_2 | X_1,X_2)$ and expressed it using the hypergeometricseries. In this paper, under some conditions, we give four other expressions ofthe Bayesian index in terms of the cumulative distribution functions of beta,$F$, binomial, and negative binomial distribution. Next, we investigate therelationship between the Bayesian index and the $p$-value of the conditionaltest with the null hypothesis $H_0: \lambda_1 \geq \lambda_2 $ versus analternative hypothesis $H_1: \lambda_1<\lambda_2 $. Additionally, weinvestigate the generalized relationship between $P(\lambda_1/\lambda_2 <c |X_1, X_2)$ and the $p$-value of the conditional test with the null hypothesis$H_0: \lambda_1/\lambda_2 \geq c$ versus the alternative $H_1:\lambda_1/\lambda_2 < c$. We illustrate the utility of the Bayesian index usinganalyses of real data. Our finding suggests that the Bayesian index canpotentially be useful in an epidemiology and in a clinical trial.

Bayesian index of superiority and the p-value of the conditional test for Poisson parameters