goodness-of-fit tests with spacings of adaptive progressively type-ii censored samples from general proportional hazard rate models

This article proposes two tests to assess the general proportional hazard rate models for adaptive progressively type-ii censored samples. these tests are based on spacings derived from the order statistics of the adaptive progressively type-ii censored sample. under the proportional hazard rate model, the distribution of the test statistics is also derived. an extensive simulation study is performed to evaluate the power of proposed tests where the underlying distribution is exponential, rayleigh, and pareto. the results indicate that the proposed tests are quite powerful. in addition, we apply these tests to analyze real-world engineering reliability datasets, highlighting their practical versatility. moreover, the point and interval estimators of the unknown parameter with the most powerful tests are derived when the adaptive progressively type-ii censored sample comes from a proportional hazard rate model