A Monte Carlo simulation study of goodness-of-fit tests for Weibull distribution based on the empirical distribution function

Document Type : Original Article

Authors

Seyed Qasim Alavi

Hadi Alizadeh Noughabi

Sarah Jomhoori

Department of Statistics, University of Birjand, Iran

10.22067/smps.2024.45177

Abstract

The Weibull distribution is widely used in reliability as a model for time to failure. In this paper, we investigate goodness-of-fit tests based on the empirical distribution function and apply them to test the validity of the Weibull model. We use the maximum likelihood estimator to estimate the scale and shape parameters of the distribution.  A Monte Carlo simulation study is employed to determine the critical values and the actual size of the considered tests. The power values of the tests are computed and compared with each other.  A real data example is used to illustrate the proposed tests.

Keywords

Empirical distribution function

Goodness-of-fit

Maximum likelihood estimates

Monte Carlo simulation

Test ‎power

Weibull distribution‎

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