A reduced new modified Weibull distribution

ABSTRACT

The author proposes a reduced version, with three parameters, of the new modified Weibull (NMW) distribution in order to avoid some estimation problems. The mathematical properties and maximum-likelihood estimation of the reduced version are studied. Four real data sets (complete and censored) are used to compare the flexibility of the reduced version versus the NMW distribution. It is shown that the reduced version has the same desirable properties of the NMW distribution in spite of having two less parameters. The NMW distribution did not provide a significantly better fit than the reduced version.

KEYWORDS:

• Hazard rate function
• maximum-likelihood estimation
• Weibull distribution.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05

Acknowledgments

The author would like to thank the editor and the referees for careful reading and for their comments and suggestions which improved the paper. The author is grateful to Dr Saralees Nadarajah for reviewing the English and improving the presentation and the motivation (part of Section 1) of this paper. Also, he would like to thank Dr. Edwin Ortega who sent the serum-reversal data set.