Inference on the parameters of two Weibull distributions based on record values

Abstract

The Weibull distribution is a very applicable model for the lifetime data. Therefore, comparing the parameters of two Weibull distributions is very important. However, there is not an appropriate method for comparing the shape or scale parameters in the literatures based on record values. In this paper, we have proposed a simple exact method for testing and constructing confidence interval for the ratio of shape parameters in two Weibull distributions. In addition, a simple exact method is proposed for inference about the common shape parameter. For comparing the scale parameters, we use the concepts of generalized confidence interval and generalized p value, and derive approaches when the shape parameters are equal or unequal. Also, we give a generalized approach for inference about the common scale parameter. At the end, we investigate inference about stress–strength reliability. Simulation results show that proposed approaches are satisfactory. All approaches are illustrated using a real example.