### Abstract

The determination of maximum likelihood estimators for the three-parameter Weibull model is usually considered a nontrivial problem, because of the nonlinear likelihood equations. Despite the availability of a large number of algorithms that tackle this problem, there is considerable dissatisfaction among practitioners, who report an inability to conveniently determine the desired MLE's (e.g. Adatia and Chan, 1985; Sinha and Sloan, 1988). We therefore review several existing algorithms for obtaining these estimators and investigate the causes of failure and some computational difficulties associated with these procedures. We find that a simple procedure outlined by Lawless (1982) is the only one that is guaranteed to yield parameter estimates that maximize the likelihood function for any sample. We describe this procedure in detail with modifications to inprove its efficiency. The method is based on firsi principles and requires less computational effort than most other schemes. Several examples from the literacure are used to rlluscraie the difficulties encouniered by ocher mezhods.

Original language | English |
---|---|

Pages (from-to) | 1037-1057 |

Number of pages | 21 |

Journal | Communications in Statistics - Simulation and Computation |

Volume | 18 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 1989 |

Externally published | Yes |

### Fingerprint

### Keywords

- estimation procedures
- maximum likelihood estimators
- three-parameter Weibull
- Weibull distribution

### ASJC Scopus subject areas

- Modelling and Simulation
- Statistics and Probability

### Cite this

*Communications in Statistics - Simulation and Computation*,

*18*(3), 1037-1057. https://doi.org/10.1080/03610918908812805

**On the determination of three-parameter weibull mle's.** / Panchang, Vijay G.; Gupta, Ramesh C.

Research output: Contribution to journal › Article

*Communications in Statistics - Simulation and Computation*, vol. 18, no. 3, pp. 1037-1057. https://doi.org/10.1080/03610918908812805

}

TY - JOUR

T1 - On the determination of three-parameter weibull mle's

AU - Panchang, Vijay G.

AU - Gupta, Ramesh C.

PY - 1989/1/1

Y1 - 1989/1/1

N2 - The determination of maximum likelihood estimators for the three-parameter Weibull model is usually considered a nontrivial problem, because of the nonlinear likelihood equations. Despite the availability of a large number of algorithms that tackle this problem, there is considerable dissatisfaction among practitioners, who report an inability to conveniently determine the desired MLE's (e.g. Adatia and Chan, 1985; Sinha and Sloan, 1988). We therefore review several existing algorithms for obtaining these estimators and investigate the causes of failure and some computational difficulties associated with these procedures. We find that a simple procedure outlined by Lawless (1982) is the only one that is guaranteed to yield parameter estimates that maximize the likelihood function for any sample. We describe this procedure in detail with modifications to inprove its efficiency. The method is based on firsi principles and requires less computational effort than most other schemes. Several examples from the literacure are used to rlluscraie the difficulties encouniered by ocher mezhods.

AB - The determination of maximum likelihood estimators for the three-parameter Weibull model is usually considered a nontrivial problem, because of the nonlinear likelihood equations. Despite the availability of a large number of algorithms that tackle this problem, there is considerable dissatisfaction among practitioners, who report an inability to conveniently determine the desired MLE's (e.g. Adatia and Chan, 1985; Sinha and Sloan, 1988). We therefore review several existing algorithms for obtaining these estimators and investigate the causes of failure and some computational difficulties associated with these procedures. We find that a simple procedure outlined by Lawless (1982) is the only one that is guaranteed to yield parameter estimates that maximize the likelihood function for any sample. We describe this procedure in detail with modifications to inprove its efficiency. The method is based on firsi principles and requires less computational effort than most other schemes. Several examples from the literacure are used to rlluscraie the difficulties encouniered by ocher mezhods.

KW - estimation procedures

KW - maximum likelihood estimators

KW - three-parameter Weibull

KW - Weibull distribution

UR - http://www.scopus.com/inward/record.url?scp=0040494985&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040494985&partnerID=8YFLogxK

U2 - 10.1080/03610918908812805

DO - 10.1080/03610918908812805

M3 - Article

AN - SCOPUS:0040494985

VL - 18

SP - 1037

EP - 1057

JO - Communications in Statistics Part B: Simulation and Computation

JF - Communications in Statistics Part B: Simulation and Computation

SN - 0361-0918

IS - 3

ER -