NEUTROSOPHIC EXTENSION OF THE NEGATIVE BINOMIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS TO INTERVAL-VALUED DATA

In real world while addressing the challenges of ambiguity and vagueness, the problems call for a scientific approach to quantify the uncertainties. The negative binomial distribution, a cornerstone in classical probability theory, traditionally examines the probability of achieving the kth success in n trials, following failures, with precise observations. However, the available literature does not address the occurrence of observations in the intervals and hence the handling of interval-valued data remained unattended. This study introduces the neutrosophic negative binomial distribution which is extended from the classical version by incorporating both indeterminacy and crisp intervals. We derive various properties of this generalized distribution which includes; characteristic function, probability function and moment generating function. This study also presents the reliability analysis metrics like cumulative hazard rate, Mills ratio, survival hazard rate, odds ratio and reversed hazard rate. This study explores the order statistics for neutrosophic negative binomial distribution, encompassing with joint, maximum, minimum and median order statistics. Special case studies are discussed which demonstrate the application of the proposed distribution, paving the way for addressing complex problems that combine conventional approaches with non-precisely determined information.