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Assessment of Scale Variable of Log-Gamma Distribution: A Bayesian Technique

Gambo S. A. , Hussain Y. , Abba S. A. , Isa I., Luqman A

Abstract

The aim of this paper is to estimate scale parameter ? of Log Gamma distribution by using inverse Gamma and inverse Chi-Square priors. The measures of loss function; Squared error loss function (SELF) and Quadratic loss function (QLF) are compared through the estimates of the scale parameter ? for best results. Wolfram Mathematica 11 was used for the analysis. The results showed that estimates of the scale parameter decrease with increase in sample size tending to the actual value of the scale parameter. This indicates an increase in the estimate of shape parameter under loss functions being considered. However, inverse chi square prior outperforms inverse gamma prior. The posterior risks for QLF are least compared to those under SELF. The Quadratic loss function therefore, appeared to be better than Squared error loss function.

Keywords

Informative PriorPosteriorLoss Function and Wolfram Mathematica 11

References

Ahmad. K, Ahmad S.P, and Ahmed. A. (2016). “Classical and Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution” Journal of Probability and Statistics, vol.4, no.2, pp.1–8, Dikko and Matthew (2018). “Bayesian Approach to Estimation of Scale Parameter of FrechetDistribution”. Bayero Journal of Pure & Applied Sciences. Feroze. N and Yaseen. W (2015a). “Left censored Nakagami distribution under Bayesian framework”, Sci. Int. (Lahore), 27(2), 945-948 Feroze. N and Yaseen. W (2015b). “Posterior Analysis of Nakagami distribution under differen Loss functions”, Sci. Int. (Lahore), 27(3) ,1819-1824 Innocent (2020). “Bayesian Analysis of Weibull-Lindly Distribution Using Different Loss Functions”. Asian Journal of Advanced Research and Report. 8(4): 28-41, 2020. Loaiy and Huda (2019). “Bayesian Estimation for Two Parameters of Gamma Distribution Under Precautionary Loss Function”. Almustansiriya University Dept. of Mathematics.

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