A new goodness-of-fit test for type-I extreme-value and 2-parameter weibull distributions with estimated parameters

Abstract

On the basis of the Kolmogorov-Smirnov (K-S), Cramer-von Mises (C-M) and Anderson- Darling (A-D) statistics, a new statisticL_n , is developed and applied for testing the goodness-of-fit of Type-I extreme-value and 2-parameter Weibull distributions with estimated parameters. Maximum likelihood estimators (MLEs) and graphical plotting techniques (GPTs) are used to estimate the population parameters from a complete sample. The critical values of the new statistic are calculated using Monte Carlo simulation, in which 1,000,000 sets of samples for each sample size of 3(1)20,25(5)50, and 60(10)100 are generated. Moreover, a power study is conducted to investigate the power of the new statistic for goodness-of-fit tests when the population parameters are estimated hy the MLEs and GPTs. Monte Carlo simulation provides the power results using 10,000 repetitions for each ample size of 5, 10, 25, and 40. The power of the new statistic is compared with those of the K-S, C-M, A-D, as well as other statistics. The power comparisons indicate that the new statistic coupled with the GPTs is the most powerful goodness-of-fit test among the competitors.

Keywords:

• Goodness-of-fit test
• Kolomogorov-Smirnov
• Cramer-von Mises
• Anderson-Darling
• Type-I extreme-value distribution
• 2-parameter Weibull distribution