Comparison of loss functions for estimating the scale parameter of log-normal distribution using non-informative priors

Year 2016, Volume: 45 Issue: 6, 1831 - 1845, 01.12.2016

Akbar Ali Khan Muhammad Aslam Zawar Hussain Muhammad Tahir

Abstract

The estimation of parameters of distributions is a core topic in the
literature on Statistical methodology. Many Bayesian and classical approaches have been derived for estimating parameters. In this study,
Bayesian estimation technique is adopted for the comparison of two
non-informative priors and six loss functions to estimate the scale parameter of Log-Normal distribution assuming fixed values of location
parameter. The main purpose of this study is to search for a suitable
prior when no prior information is available and to look for an appropriate loss function for estimation of the scale parameter of Log-Normal
distribution. Through simulation study, comparisons are made on the
basis of the posterior variances, coefficients of skewness, ex-kurtosis and
Bayes risks. The simulation results are verified through a real data set
of lung cancer patients.

Keywords

Prior distribution, Posterior distribution, Log-Normal distribution, Inverted Gamma distribution

References

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