A reduced new modified Weibull distribution

TL;DR

This paper introduces a simplified three-parameter version of the new modified Weibull distribution, maintaining its flexibility and properties while reducing estimation complexity, and demonstrates its comparable or superior fit on real data.

Contribution

A reduced three-parameter Weibull distribution is proposed, simplifying estimation while preserving key properties and flexibility of the original five-parameter version.

Findings

Reduced version has similar properties to NMW distribution.

Reduced version fits real data as well as or better than NMW.

Fewer parameters improve estimation without loss of flexibility.

Abstract

In this paper, we propose a reduced version of the new modified Weibull (NMW) distribution due to Almalki and Yuan \cite{meNMW} in order to avoid some estimation problems. The number of parameters in the NMW distribution is five. The number of parameters in the reduced version is three. We study mathematical properties as well as maximum likelihood estimation of the reduced version. Four real data sets (two of them complete and the other two 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 for any of the four data sets.