Open AccessGeneralized exponential Marshall-Olkin distribution
Author(s) -
Reza Mohammad,
Dian Lestari,
S. Devila
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1725/1/012100
Subject(s) - natural exponential family , mathematics , weibull distribution , generalized beta distribution , gamma distribution , laplace distribution , exponential distribution , distribution fitting , statistics , generalized integer gamma distribution , log cauchy distribution , exponential function , akaike information criterion , exponential family , exponentiated weibull distribution , generalized gamma distribution , inverse chi squared distribution , mathematical analysis
The distribution of generalized exponential was invented by Rameshwar D. Gupta and Debasis Kundu in 2007. The distribution was the result of a generalized transformation of the exponential distribution. This paper explained the generalized exponential Marshall-Olkin distribution which is the result of the expansion of the generalized exponential distribution using the Marshall-Olkin method. The generalized exponential Marshall-Olkin distribution has a more flexible form than the previous distribution, especially in its hazard function which has various forms so that it can represent survival data better. The flexibility characteristic is due to the addition of new parameters to the generalized exponential Marshall-Olkin distribution. We explained some characteristics of the Marshall-Olkin generalized exponential distribution such as the probability density function (PDF), cumulative distribution function (CDF), survival function, hazard function, mean, and moments. Parameter estimation was conducted using the maximum likelihood method. In the application, it was shown data with generalized exponential Marshall-Olkin (GEMO) distribution. The GEMO distribution was modelled to the waiting time data until the damage to a lamp. The data was taken from Aarset data (1987). The results of modelling the waiting time data until the damage to a lamp on the distribution of GEMO and was compared to the distribution of alpha power Weibull. A comparison of models using Akaike information criteria (AIC) and Bayesian information criteria (BIC) shows that the distribution of GEMO is more suitable in modelling the lamp damage waiting time data than the distribution of alpha power Weibull.