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Kavya-Manoharan DUS Family of Distributions with Diverse Applications |
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PP: 587-616 |
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doi:10.18576/jsap/140608
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Author(s) |
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Edwin Ikechukwu Obisue,
Chiemeka Nwankwor Okoro,
Okechukwu J. Obulezi,
Gaber Sallam Salem Abdalla,
Ehab M. Almetwally,
Abdoulie Faal,
Mohammed Elgarhy,
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Abstract |
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| In this work, a new family of distributions is proposed without adding any new parameters to any known baseline distribution. This family, the Kavya-Manoharan Dinesh-Umesh-Sanjay (KM-DUS) family, is the mixture of the Kavya-Manoharan (KM) and the Dinesh-Umesh-Sanjay (DUS) families. A new two-parameter distribution, the KM-DUS- Weibull (KM-DUS-W), is built on the foundation of the Weibull distribution to model time-to-event data sets. The KM-DUS-W is a more convenient and computationally tractable alternative to the Weibull distribution and a parsimonious but effective modeling aid for survival and reliability data. The primary statistical properties including the probability density function, cumulative distribution function, quantile function, moments, order statistics and entropy are obtained. Parameter estimation is accomplished with numerous classical and Bayesian estimators. Maximum Likelihood, Least Squares, Weighted Least Squares, Maximum Product Spacing (MPS), Crame ́r-von Mises, Anderson-Darling, Right-Tailed Anderson-Darling, Percentile estimation, and Bayesian approaches under Squared Error, LINEX, and General Entropy loss functions. Amongst these, the non-Bayesian ones always provide the most efficient estimates for any sample size. Applicability of the KM-DUS-RIW distribution in real life is illustrated through failure times of the 84 Aircraft Windshield, COVID-19 death rate for Angola between 14/06/2020 and 20/2/2022, carbon fibers breaking stress and 30 observations of the March precipitation pattern (in inches) in Minneapolis/St Paul. Comparative goodness-of-fit of log-likelihood, AIC, BIC, HQIC, and Kolmogorov-Smirnov statistics give evidence that KM-DUS-W model is better performing than other alternative models like Weibull, Gumbel, log-normal, new generalized logistic-x transformed exponential and Burr type XII distributions. These results give support to the KM-DUS-W distribution as an alternative option for modeling complex lifetime data. |
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