Investigation of half-normal model using informative priors under Bayesian structure

Sania Khawar Kiani; Muhammad Aslam; M. Ishaq Bhatti

doi:https://doi.org/10.59170/stattrans-2023-049

Investigation of half-normal model using informative priors under Bayesian structure

Sania Khawar Kiani Riphah College of Rehabilitation Sciences, Riphah International University, Islamabad, Pakistan ORCID:https://orcid.org/0000-0002-7744-3593 , Muhammad Aslam Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan ORCID:https://orcid.org/0000-0003-3355-2330 , M. Ishaq Bhatti SBE-UBD, Universiti Brunei Darussalam, Brunei & LBS, La Trobe University, Melbourne, Australia ORCID:https://orcid.org/0000-0002-5027-7871 Statistics in Transition new series, vol. 24, 2023, 4, pages: 19-36 Published online: 8 September 2023 https://doi.org/10.59170/stattrans-2023-049

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ARTICLE

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ABSTRACT

This paper considers properties of half-normal distribution using informative priors under the Bayesian criterion. It employs the squared root inverted gamma, Chi-square and Rayleigh distributions as the prior distribution to construct the Posterior distributions of the respective distributional parameters. Hyperparameters are elicited via prior predictive distribution. The properties of posterior distribution are studied, and their graphs are presented using a real data set. A comprehensive simulation scheme is conducted using informative priors. Bayes estimates are obtained using the loss functions (squared error loss function, modified loss function, quadratic loss function and Degroot loss function). Statistical inferences interval estimates and Bayesian hypothesis testing are presented to demonstrate the usefulness of the study.

KEYWORDS

informative prior, squared root inverted gamma distribution (SRIG), Bayesian hypothesis testing, loss functions.

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