Abstract
Abstract We obtained a new generalization of Lindley-Quasi Xgamma distribution by adding weight parameter to it through weighting technique and have shown the flexibility of proposed model. Expression for reliability measures, order statistics, Bonferroni curves & indices, Renyi entropy along with some other important properties are derived. Maximum likelihood estimation method is put to use for estimation of unknown parameters of proposed model. Simulation study for checking the performance of maximum likelihood estimates and for model comparison is carried out. Proposed model and its related models are fitted to real life data sets and goodness of fit measure Kolmogorov statistic & p-value, loss of information criteria’s AIC, BIC, AICC & HQIC are computed through R software to check the applicability of proposed model in real life. The significance of weight parameter is also tested by using likelihood ratio test for both randomly generated data as well as real life data.
Highlights
Probability models are and have been generalized for providing more flexibility in terms of hazard rate, reliability, prediction and moments
One of the method employed for generalizing probability models by adding weight parameter is weighting technique
Different criteria’s of goodness of fit like AIC, BIC, AICC, HQIC and K-S distance have been computed by using R software for both the data sets and it has been observed from Tables 8 and 9 that proposed model possesses lesser AIC, BIC, AICC, HQIC & K-S distance values as compared to Lindley Quasi Xgamma distribution, Quasi Lindley distribution, Exponential distribution and Quasi Akash distribution for both the data sets
Summary
Probability models are and have been generalized for providing more flexibility in terms of hazard rate, reliability, prediction and moments. Dar and Para [2] introduced a new generalization of Ishita distribution and obtained vital mathematical properties of the distribution along with applications of the proposed model. Patil and Rao [5] introduced weighted distributions and size biased sampling with applications to wild life populations and human families and obtained its properties. Wani and Shafi [6] introduced Poisson Pranav distribution and obtained its various mathematical properties along with obtaining applications of the proposed model. Wani, Bilal and Akhtar [8] introduced weighted Quasi Xgamma distribution and studied its properties and applications. Wani, Shafi and Sheikh [9] introduced Lindley-Quasi Xgamma Distribution (LQXD). In this paper we have obtained weighted version of Lindley-Quasi Xgamma (LQXD) distribution with p.d.f given in (1.1)
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