Neutrosophic New Odd Weibull-Weibull Distribution with Heart Pulse Count Data Application

This paper presents a new probability distribution known as the "Neutrosophic New Odd Weibull-Weibull Distribution (NNOWW)" by combining the proposed New Odd Weibull-Weibull (NOWW) distribution with the neutrosophic logic (the direct method of this logic). The distribution is presented in two theoretical frameworks. The derivation of several main distribution functions, along with their properties, is presented, accompanied by both theoretical and graphical representations of these properties. Parameters are estimated using three different methods, with Monte Carlo simulations conducted for various sample sizes to determine the estimation efficiency and the most suitable sample size for applying the distribution to real data. An applied framework tests its efficiency on real data representing the heart rate of 50 patients. The model was developed within this logic framework to define truth, falsity, and uncertainty in the data. The model was compared with five other neutrosophic distributions using criteria such as AIC, BIC, CAIC, and HQIC. The results showed a clear superiority of the NNOWW model across all indicators, confirming its accuracy and ability to represent uncertain data. Analytical graphs support this superiority. This model is recommended for use in medical fields and for analyzing Neutrosophic data.