Prediction from Transmuted Rayleigh Distribution in the Presence of Outliers

Abstract

The quality of the procedures used in statistical analysis depends largely on the assumed probability distribution. However, there are still many problems with data that do not follow any of the classical distributions; therefore, researchers have developed many standardized probability distributions by generalizing or transforming them. Transmuted Rayleigh distribution extends the Rayleigh distribution in the analysis of data and provides larger flexibility in modeling real data. In this article, Bayesian predictive intervals for order statistics of future observations from this distribution are obtained in the presence of outliers when the scale parameter is unknown. The slippage outlier model is utilized in addition to the two-sample prediction scheme. We shall consider two cases: (i) a single outlier in the informative sample and (ii) multiple outliers in the future sample. Numerical computations are obtained to illustrate the effect of outliers on the Bayesian predictive intervals.