Abstract
In this paper, we have proposed a new version of power lindley distribution known as weighted power lindley distribution. The different structural properties of the newly model have been studied. The maximum likelihood estimators of the parameters and the Fishers information matrix have been discussed. It also provides more flexibility to analyze complex real data sets. An application of the model to a real data set is analyzed using the new distribution, which shows that the weighted power Lindley distribution can be used quite effectively in analyzing real lifetime data.
Highlights
The weighted distributions are applied in various research areas related to biomedicine, reliability, ecology and branching processes
We introduce a new distribution with three parameters, namely as weighted power Lindley (WPL) distribution, with the hope that it will attract many applications in different disciplines such as reliability, survival analysis, biology and others
In order to compare the WPL distribution with the PL, Exponential and Lindley distributions, we consider the criteria like Bayesian information criterion (BIC), Akaike Information Criterion (AIC), Akaike Information Criterion Corrected (AICC) and -2 logL
Summary
The weighted distributions are applied in various research areas related to biomedicine, reliability, ecology and branching processes. The concept of weighted distributions is traceable to the work of Fisher (1934) in respect of his studies on how methods of ascertainment can affect the form of distribution of recorded observations Later, it was introduced and formulated in a more general way by Rao (1965) with respect to modelling statistical data where the routine practice of using standard distributions for the purpose was dismissed as inappropriate. Das and Kundu (2016) discussed on various statistical properties of the weighted exponential distribution and its length biased version. We introduce a new distribution with three parameters, namely as weighted power Lindley (WPL) distribution, with the hope that it will attract many applications in different disciplines such as reliability, survival analysis, biology and others. The real life time data has been fitted and the fit has been found to be good
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