Mathematical development of the new Sine type II generalized Topp-Leone exponential distribution with applications to biomedical data

The development of flexible probability distributions remains an essential aspect of modern statistical modeling, particularly in capturing complex patterns observed in real-life data. In this study, a new continuous distribution, referred to as the New Sine II Generalized Topp-Leone Exponential (NSTIIGTLE) distribution, is introduced. The proposed model is constructed by integrating the sine Generator with the Type II generalized Topp-Leone family, using exponential distribution as the baseline. Key statistical properties of the new distribution are derived, including explicit expressions for the pdf, cdf, survival function, and hazard rate function. In addition, important characteristics such as moments, moment generating function, and quantile function are obtained to facilitate practical implementation and interpretation. Parameter estimation is carried out using the maximum likelihood estimation (MLE) and the maximum product of spacing MPS) methods, and the performance of the estimators is examined through a simulation study under varying sample sizes. The results indicate that the estimators are consistent and exhibits improve accuracy as the sample size increases. To demonstrate the practical relevance, the proposed distribution is applied to biomedical data, where it is compared with several existing competing models using standard goodness-of-fit measures such as AIC, BIC, and LL. The findings reveal that the NSTIIGTLE distribution provides a superior fit, highlighting its potential as a reliable tool for modeling lifetime data and other biomedical phenomena.