A general class of flexible Weibull distributions

We consider a linear combination of two logarithms of cumulative hazard functions and propose a general class of flexible Weibull distribution functions which includes some well-known modified Weibull distributions (MWDs). We suggest a very flexible Weibull distribution, which belongs to the class,...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2018-02, Vol.47 (4), p.767-778
Main Authors: Park, Sangun, Park, Jiwhan
Format: Article
Language:English
Subjects:
Bathtub shape
Current distribution
Distribution functions
Economic models
goodness of fit
hazard function
Logarithms
maximum likelihood estimate
Maximum likelihood estimation
Parameter estimation
reliability
Weibull distribution
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Summary:We consider a linear combination of two logarithms of cumulative hazard functions and propose a general class of flexible Weibull distribution functions which includes some well-known modified Weibull distributions (MWDs). We suggest a very flexible Weibull distribution, which belongs to the class, and show that its hazard function is monotone, bathtub-shaped, modified bathtub-shaped, or even upside-down bathtub-shaped. We also discuss the methods of least square estimation and maximum likelihood estimation of the unknown parameters. We take two illustrated examples to compare the suggested distribution with some current MWDs, and show that the suggested distribution shows good performances.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2015.1118509