Neutrosophic Kies Distribution with Basic Properties and Engineering Applications

Abstract

In this study, we introduce the Neutrosophic Kies Distribution (NKD) by extending the classical Kies distribution to neutrosophic statistics for capturing parameter uncertainty with interval-valued parameters. The important properties of the NKD are investigated such as closed-form quantile and reliability functions, hazard rate, moments, and mean residual life. We consider estimation methods with neutrosophic maximum likelihood and moments. In particular, MLE is shown to have a nice closed-form solution. Numerical studies show that the estimators provide valid interval estimates and cover true values with nominal probability level under irreducibly uncertain parameter space. Consistency, normality, and asymptotic efficiency results are derived. Application examples from engineering studies (bank waiting times, patient relief times, aircraft window strength) show superior performance of the NKD compared to other competitors (Exponential, Weibull, Lindley). NKD yields the smallest AIC scores and the best fits according to the goodness-of-fit p-values. Hazard rate function of the NKD is an increasing function; h(t) = λ/(1-t)².