Abstract
In the present paper, we propose the new Janardan-Power Series (JPS) class of distributions, which is a result of combining the Janardan distribution of Shanker et.al (2013) with the family of power series distributions. Here, we examine the fundamental attributes of this class of distribution, including the survival, hazard and reverse hazard functions, limiting behavior of the cdf and pdf, quantile function, moments and distribution of order statistics. Moreover, the particular case of the JPS distribution such as the JanardanBinomial (JB), Janardan-Geometric (JG), Janardan-Poisson (JP) and the Janardan-Logarithmic (JL) distributions, are introduced. In addition, the JP distribution is analyzed in details. Eventually, an example of the proposed class applied on some real data set.
Highlights
Modeling lifetime data is considered in the area of survival analysis, in which the lifetime of biological organisms or mechanical systems is investigated
The underlying logic and assumptions behind these models is that a lifetime of a system with Ncomponents and the positive continuous random variable,Xi, which designates the lifetime of the ithcomponent,can be described by a nonnegative random variable X = min( X1, ... , XN) orX = max( X1, ... , XN),depending on whether the components are series or parallel
The power series class of distributions was examined and derived by Noack (1950), in which N is a discrete random variable depending on the class of power series distributions with probability mass function anλn C(λ) where an ≥ 0 for all n = 1,2, ... which only relies on n,C( λ) = ∑∞n=1 anλnandλ >0, is fixed in a way that C( λ) is finite and its first derivative with reference to λ are determined and indicated byC′(. )
Summary
Modeling lifetime data is considered in the area of survival analysis, in which the lifetime of biological organisms or mechanical systems is investigated. Many recently introduced distributions have the capability to model these types of data appropriately. The power series class of distributions was examined and derived by Noack (1950), in which N is a discrete random variable depending on the class of power series distributions with probability mass function. ). Many novel models have been recently developed by authors utilizing the power series class of distributions, which some of them have been designed as a combination of some well-established distributions and the power series class of distributions. It has been proved that the Janardan distribution is a better model compared to the one parameter Lindley distribution, in terms of analyzing waiting time, survival time and grouped mortality data.
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