## Brazilian Journal of Probability and Statistics

### Bayesian analysis based on the Jeffreys prior for the hyperbolic distribution

#### Abstract

In this work, we develop Bayesian analysis based on the Jeffreys prior for the hyperbolic family of distributions. It is usually difficult to estimate the four parameters in this class: to be reliable the maximum likelihood estimator typically requires large sample sizes of the order of thousands of observations. Moreover, improper prior distributions may lead to improper posterior distributions, whereas proper prior distributions may dominate the analysis. Here, we show through a simulation study that Bayesian methods based on Jeffreys prior provide reliable point and interval estimators. Moreover, this simulation study shows that for the absolute loss function Bayesian estimators compare favorably to maximum likelihood estimators. Finally, we illustrate with an application to real data that our methodology allows for parameter estimation with remarkable good properties even for a small sample size.

#### Article information

Source
Braz. J. Probab. Stat., Volume 26, Number 4 (2012), 327-343.

Dates
First available in Project Euclid: 3 July 2012

https://projecteuclid.org/euclid.bjps/1341320246

Digital Object Identifier
doi:10.1214/11-BJPS142

Mathematical Reviews number (MathSciNet)
MR2949082

Zentralblatt MATH identifier
1319.62060

#### Citation

Fonseca, Thaís C. O.; Migon, Helio S.; Ferreira, Marco A. R. Bayesian analysis based on the Jeffreys prior for the hyperbolic distribution. Braz. J. Probab. Stat. 26 (2012), no. 4, 327--343. doi:10.1214/11-BJPS142. https://projecteuclid.org/euclid.bjps/1341320246

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