Theoretical aspects and simulation with the application of a new two parameter distribution.

This research introduces a new two-parameter distribution (NTPD). The probability density function of the NTPD exhibits distinctive characteristics, making it a valuable tool for modelling various real-world phenomena. Several key statistical properties of the distribution, including the mode, reliability function, hazard function, moments, moment generating function, Rényi entropy, fuzzy reliability, stochastic ordering, and quantile function, are derived explicitly. The model parameters are estimated using sixteen classical methods, and their performance is assessed through a comprehensive simulation study. Applications to datasets with complex behaviors, such as high skewness and peakedness, from environmental science, biomedical science, and reliability engineering demonstrate that the NTPD provides a superior fit compared to several established distributions, including the Lindley, XLindley, modified Lindley, sine Lindley, and exponentiated inverse Rayleigh distributions.