Point estimation and two new goodness of fit tests for the scale family based on general progressively Type-II censored samples

In this paper, we obtain an analytic and explicit estimator of the scale parameter using pivotal method and propose two new goodness of fit tests for the scale family based on general progressively Type-II censored samples. The properties about the test statistics are studied. Furthermore, we apply our methods to some specific life distributions for illustration. Moreover, we obtain critical values by simulations and compare the power of the two tests against various alternatives under many censoring schemes. We also obtain the empirical significance levels thorough Monte Carlo simulation. We do the comparison of the proposed estimator with the existing estimators given in the literature by means of a power study. The influence of the parameter in the alternative distribution to power is explored. The simulation results are presented using data visualization. We conclude that the estimator we derive and tests we propose perform well in many cases. Finally, a numerical example is presented.