A general class of flexible Weibull distributions

Sangun Park; Jiwhan Park

doi:10.1080/03610926.2015.1118509

A general class of flexible Weibull distributions

Sangun Park, Jiwhan Park

Department of Applied Statistics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	767-778
Number of pages	12
Journal	Communications in Statistics - Theory and Methods
Volume	47
Issue number	4
DOIs	https://doi.org/10.1080/03610926.2015.1118509
Publication status	Published - 2018 Feb 16

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea government(MOE) (No. 2015R1D1A1A01056578) and by the Korea government (MSIP) (NRF-2015R1A2A1A15051493).

Publisher Copyright:
© 2018 Taylor & Francis Group, LLC.

All Science Journal Classification (ASJC) codes

Statistics and Probability

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10.1080/03610926.2015.1118509

Cite this

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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.",

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N2 - 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.

AB - 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.

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A general class of flexible Weibull distributions

Abstract

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