A Neutrosophic Extension of the Inverse Gamma Distribution: Properties and Applications

This paper proposes a new the neutrosophic inverse gamma (NIG) distribution which is a generalization of the classical Inverse Gamma (IG) model to deal with vagueness, uncertainty and indeterminacy observed in healthcare and survival data. Since the traditional models are limited by rigid fixed parameters and are not capable of well approximating the fact that all imprecision arising from measurement errors, missing values, conflicting expert's assessments should be left in the imprecision of human judgement. The proposed model is more flexible and realistic, since shape and scale parameters can vary in certain intervals, by using neutrosophic logic. Some certain characteristics of the NIG distribution, such as the probability density function (PDF), cumulative distribution function (CDF), and moments are obtained and studied. The estimation techniques are also constructed for neutrosophic data. With simulations, random samples were generated from the model and the model’s ability to capture uncertainty in the simulated data is illustrated. Simulated results indicate that NIG is providing more robust and informative parameter estimates as long as sample size increases. Eventually, solar sector industrial data is employed to validate the proposed methodology and highlights its effectiveness in decision making.