On a New Generalized Mixture of Weibull-Rayleigh Distribution
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Authors
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Smriti Sikha Sarma
North-Eastern Hill University, Shillong
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Bishal Gurung
North-Eastern Hill University, Shillong
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Bhanita Das
North-Eastern Hill University, Shillong
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Sajadul Hussain
Dibrugarh University, Dibrugarh
Keywords:
Weibull distribution; Rayleigh distribution; Weighted mixture; Survival function; Distribution family.Abstract
In this paper, a novel generalized distribution has been proposed which is obtained through the framework of a
Two distributions weighted by a parameter
are combined to create the -weighted mixture family (-WM). -weighted mixture family, which provides substantial flexibility for
modelling a diverse range of intricate phenomena. The new four parameter distribution is referred as θ-Weighted Mixture Weibull-Rayleigh (-WMWR) distribution, resulting from the combination of Weibull and Rayleigh distributions. The characterization and numerous statistical properties
are derived, including the reliability function, hazard rate function, quantile function, mean residual life, mean inactivity time, rth moment, Rényi
entropy, and order statistics. Finally, the applicability and effectiveness of the proposed distribution are demonstrated using real-life datasets, and its
performance is compared with existing models such as the Alpha-Power Exponentiated Inverse Rayleigh (APEIR), θ-Weighted Mixture Weibull
Lomax (θ-WMWLx), and Lomax–Rayleigh (LR) distributions to highlight potential of the proposed distribution.
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