Estimation of the Parameters of Power Function Distribution based on Records

Abstract

This paper estimates the power function distribution parameters and predicts the future record values when samples are available only in the form of upper record values. We considered the maximum likelihood and Bayesian techniques for the estimation. We also construct asymptotic, bootstrap, and HPD confidence intervals for the unknown parameters. Bayes estimators are derived using the squared error loss function, entropy loss function, and Linex loss function using the Lindley approximation and importance sampling procedures. Finally, we conduct a simulation study to compare all the proposed estimation methods and analyse a real data set for illustration purposes.