A Smooth Test of Goodness-of-Fit for the Weibull Distribution: An Application to an HIV Retention Data

Collins Odhiambo, John Odhiambo, Bernard Omolo


In this study, we fit the two-parameter Weibull distribution to an HIV retention data and assess the fit using a smooth test of goodness-of-fit. The smooth test described here is a score test and is derived as an extension of the Neyman’s smooth test. Simulations are conducted to compare the power of the smooth test with the power of each of three empirical goodness-of-fit tests for the Weibull distribution. Results show that the smooth tests of order three and four are more powerful than the three empirical goodness-of-fit tests. For validation, we used retention data from an HIV care setting in Kenya.


Goodness-of-fit, Loss to follow-up, Neyman’s smooth test, Retention in HIV care, Weibull distribution.

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ISSN: 1929-6029