A general class of flexible Weibull distributions. Issue 4 (16th February 2018)

• Record Type: Journal Article
• Authors: Park, Sangun; Park, Jiwhan
• Is Part Of: Communications in statistics. Volume 47:Issue 4(2018)
• Page Start: 767
• Page End: 778
• Publication Date: 2018-02-16
• Subjects: Bathtub shape -- goodness of fit -- hazard function -- maximum likelihood estimate -- reliability.; 60E05 -- 62H05 -- 62H15; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1118509
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: 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.