The New G*Q-Logarithmic Family: Properties, Estimation Approaches and Applications
Subject Areas : StatisticsArezoo Amirzadi 1 , Ezzatallah Baloui Jamkhaneh 2 , Einolah Deiri 3
1 - Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
2 - Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
3 - Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
Keywords: تابع قابلیت اطمینان, طول عمر, نمونهگیری نقاط مهم, تبدیل لگاریتمی, برآوردگر E-بیز,
Abstract :
In this paper, we introduce a new family of lifetime distributions called the G*Q-Logarithmic family and using the maximum likelihood, Bayesian and E-Bayesian approaches, obtain the estimation of the parameters of the new family as well as analyze the corresponding reliability function. In addition, check some statistical properties such as non-central moment, incomplete moment, moment generating and quantile functions of this family and by considering the inverse Weibull baseline distribution, introduce two sub models of this family called exponential inverse Weibull-logarithmic and power inverse Weibull-logarithmic and represent the statistical properties and parameter estimations of the two new introduced models. In the following, we compare the estimation methods using the Monte Carlo simulation approach. The superiority of the new introduced family to fit real data, with some classical distributions such as gamma, Weibull , Pareto, Gompertz, Lindley, Burr XII type, inverse Weibull, Weibull Mashall-Olkin and exponentiated Weibull has also been investigated and reported.
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