Statistical inferences of a two-parameter distribution with the bathtub shape based on progressive censored sample

Abstract

This study considers the hypothesis test and interval estimation of the shape parameter of a new two-parameter distribution with the bathtub shape or increasing failure rate function under type-II progressive censoring based on the proposed m pivotal quantities. The confidence region of two parameters of this distribution is also proposed. We give one numerical example to illustrate the proposed methods. Next, the Monte Carlo simulation is done to assess the behaviour of these pivotal quantities. Lastly, we find the optimal pivotal quantity based on the criteria of highest power, minimum confidence length and the minimum confidence region.