Predictive Inference and Parameter Estimation from the Half-Normal Distribution for the Left Censored Data

Abstract

In present article, we consider predictive inference and the Bayesian estimation for the parameter assuming that the given left censored data follow the half-normal distribution. Predictive density function for a single future response, a bivariate future response, and several future responses is obtained by incorporating the posterior density function. To derive the posterior and predictive distribution result on the basis of the left censored data, a Bayesian framework was employed in conjunction with an informative prior. Also, the Bayesian structure was utilized in association with informative and uninformative priors to obtain the Bayes estimators on the basis of different loss functions. Simulated left censored samples from a half-normal distribution are utilized to interpret the results. Posterior risks of the Bayes estimators are evaluated and compared to explore the effect of prior belief and loss functions. Bayes estimators are efficient under quasi quadratic loss function using the square root gamma prior.