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

Area of Science:

• Statistics
• Probability Theory
• Neutrosophic Logic

Background:

• The need for robust statistical models to handle uncertainty in data is growing.
• Existing distributions may not adequately capture the complex nature of real-world data, especially in fields like medicine.

Purpose of the Study:

• To introduce and develop the Neutrosophic New Odd Weibull-Weibull Distribution (NNOWW).
• To evaluate the performance and applicability of the NNOWW distribution using theoretical and empirical methods.
• To compare the NNOWW model with existing neutrosophic distributions for uncertain data analysis.

Main Methods:

• Derivation of the NNOWW distribution functions and their properties.
• Parameter estimation using three distinct methods.
• Monte Carlo simulations to assess estimation efficiency across various sample sizes.
• Application and validation on real-world patient heart rate data.

Main Results:

• The NNOWW distribution was successfully derived and its properties analyzed.
• Monte Carlo simulations indicated efficient parameter estimation and identified optimal sample sizes.
• The NNOWW model significantly outperformed five other neutrosophic distributions based on AIC, BIC, CAIC, and HQIC criteria.
• The model demonstrated superior accuracy in representing uncertain heart rate data.

Conclusions:

• The NNOWW distribution is a highly accurate and efficient model for analyzing uncertain data.
• The model shows significant promise for applications in medical fields and other areas dealing with complex, uncertain datasets.
• The NNOWW model provides a valuable tool for defining truth, falsity, and uncertainty within data analysis frameworks.