A New Test Statistic to Assess the Goodness of Fit of Location-Scale Distribution Based on Progressive Censored Data

Abstract

The problem of examining how well the data fit a supposed distribution is very important, and it must be confirmed prior to any data analysis, because many data analysis methods assume a specific distribution of data. For this purpose, histograms or Q-Q plots are employed for the assessment of data distribution. Additionally, a GoF TstS utilizes distance measurements between the empirical distribution function and the theoretical cumulative distribution function (cdf) to evaluate data distribution. In life-testing or reliability studies, the observed failure time of test units may not be recorded in some situations. The GoF TstSs for completely observed data can no longer be used in progressive type II censored data (PrCsD). In this paper, we suggest a GoF TstSs and new plot method for the GoF test of symmetric and asymmetric location-scale distribution (LoScD) based on PrCsD. The power of the suggested TstSs is estimated through Monte Carlo (MC) simulations, and it is compared with that of the TstSs using the order statistics (OrSt). Furthermore, we analyzed real data examples (symmetric and asymmetric data).

Keywords

• goodness-of-fit test
• location-scale distribution
• Lorenz curve
• power
• progressive type II censored data