The Power Muth Distribution^*

* Research in this paper has been partially funded by the research projects: CTM2015-68276-R MINECO/FEDER,UE (M.V. Alba-Fernández), Diputación General de Aragón -Grupo consolidado PDIE- (P. Jodrá), FONDECYT 1130495 (H.W. Gómez) and MTM2014-55966-P of the Spanish Ministry of Economy and Competitiveness (M.D. Jiménez-Gamero).

Abstract

Muth introduced a probability distribution with application in reliability theory. We propose a new model from the Muth law. This paper studies its statistical properties, such as the computation of the moments, computer generation of pseudo-random data and the behavior of the failure rate function, among others. The estimation of parameters is carried out by the method of maximum likelihood and a Monte Carlo simulation study assesses the performance of this method. The practical usefulness of the new model is illustrated by means of two real data sets, showing that it may provide a better fit than other probability distributions.

Keywords:

• Muth distribution
• survival analysis
• estimation
• simulation
• data analysis

AMS Subject Classification:

• 60E05
• 62F10
• 33B30

Notes

* Research in this paper has been partially funded by the research projects: CTM2015-68276-R MINECO/FEDER,UE (M.V. Alba-Fernández), Diputación General de Aragón -Grupo consolidado PDIE- (P. Jodrá), FONDECYT 1130495 (H.W. Gómez) and MTM2014-55966-P of the Spanish Ministry of Economy and Competitiveness (M.D. Jiménez-Gamero).