Bounded sine hyperbolic distribution with applications to real datasets

In this paper, a novel hyperbolic trigonometric probability distribution with a bounded support on (0,1) named the bounded sine hyperbolic (BSH) distribution is proposed. It has a simple closed form cumulative distribution function (CDF). Various structural properties of the distribution are obtained, such as quantile function, moments, entropy, order statistics, reversed order statistics, upper record statistics, residual lifetime function, and reversed residual life function. The distribution exhibits a wide range of shapes with the bathtub shape of the failure rate function (FRF). The performance of the bounded sine hyperbolic distribution has been verified using both mathematical and graphical approaches. Maximum log likelihood estimation (MLE) has been utilized to estimate the unknown parametric values of the BSH distribution. To assess the consistency of the maximum likelihood estimation, a simulation study is conducted. The BSH distribution is compared with established models (unit Lindley, unit Teissier, and unit Rayleigh) using two real-world datasets. Different evaluation criterion and goodness-of-fit statistics, i.e. AIC, AICC, BIC, HQIC, CAIC, Anderson Darling (A*), Cramer Von-Mises (W*), and Kolmogorov–Smirnov (KS) tests, confirm the superiority of the BSH distribution as per numerical values provided in Tables 7 and 8. The lowest values of all these tests demonstrate that the BSH distribution outperforms other related models.