Neutrosophic Structure of Sized Biased Exponential Distribution: Properties and Applications

This study presents a novel distribution derived from the exponential distribution, referred to as the neutrosophic size-biased exponential distribution (NSBED). Various characteristics of the proposed model, including moments, skewness, and kurtosis, are investigated. Plots depicting the cumulative distribution function, density function, and other relevant functions associated with the survival analysis hazard function under indeterminacy are provided. Parameter estimates for the proposed model within the neutrosophic framework are computed. To illustrate the statistical applications of the results in handling imprecise data, a motivation is provided. A simulation analysis is conducted to validate the theoretical aspects of the proposed NSBED. Results indicate that the new distribution exhibits right skewness and shares many properties with skewed distributions. Our novel distribution outperforms the size-biased exponential distribution. Finally, a real application of the proposed model is provided to illustrate the practical implications.