Goodness-of-fit test for exponentiality based on spacings for general progressive Type-II censored data

Abstract

There have been numerous tests proposed to determine whether or not the exponential model is suitable for a given data set. In this article, we propose a new test statistic based on spacings to test whether the general progressive Type-II censored samples are from exponential distribution. The null distribution of the test statistic is discussed and it could be approximated by the standard normal distribution. Meanwhile, we propose an approximate method for calculating the expectation and variance of samples under null hypothesis and corresponding power function is also given. Then, a simulation study is conducted. We calculate the approximation of the power based on normality and compare the results with those obtained by Monte Carlo simulation under different alternatives with distinct types of hazard function. Results of simulation study disclose that the power properties of this statistic by using Monte Carlo simulation are better for the alternatives with monotone increasing hazard function, and otherwise, normal approximation simulation results are relatively better. Finally, two illustrative examples are presented.

Keywords: Exponential distribution; Monte Carlo simulation; general progressive Type-II censoring; goodness-of-fit; spacings.