Goodness-of-fit Test For The Location-scale Distributions Based On Progressively Type-Ⅱ Censored Sample

Goodness-of-fit test is not only an important part of the basic statistics, but also closely related with the application. Pakyari et al.(2011) discussed the goodness-of-fit test for the location-scale distributions when the available sample is progressively Type-Ⅱ censored and gave several test statistics. Monte Carlo simulation shows that the power values of the proposed tests outnumber the existing test T proposed by Balakrishnan et al.(2004) in some early censored case.Based on the idea of transformation and weighting, we modified two tests Tmin(1) and Tmin(2), which are proposed due to Pakyari et al.(2011). To assess the power properties of the modified tests, a Monte Carlo study was conducted to estimate the power under different alternatives. Under the simple null hypothesis, the power values of the modified tests outperform Tmin(1) and Tmin(2) in most cases. Respectively, for the early censoring schemes, the proposed tests are always perform better than Tmin(1) and Tmin(2); when m is large, WMTmin(1) and WMTmin(2) perform better than Pmin(1) and Tmin(2) in multiple censored cases. Under the composite null hypothesis, the modification is also effective.Additionally, we present another test W for the location-scale distributions based on progressively Type-Ⅱ censored sample and derive the exact null distribution when under the simple null hypothesis. Under the simple null hypothesis, Monte Carlo simulation reveals that the W-statistic outperform the T-statistic in most cases. Respectively, when testing the normal distribution, the power values of the new statistic always exceed the values of the T-statistic; when testing the Gumbel distribution, for the late censoring, the new statistic also perform better than the T-statistic. Under the composite null hypothesis, when testing the normal distribution, for the late censoring, the new statistic performs better than the T-statistic.