In this paper, a new probability distribution, based on the family of hyperbolic cosine distributions is proposed and its various statistical and reliability characteristics are investigated. The new category of HCF distributions is obtained by combining a baseline F distribution with the hyperbolic cosine function. Based on the base log-logistics distribution, we introduce a new distribution so-called HCLL and derive the various properties of the proposed distribution including the moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and stress-strength parameter. Estimation of the parameters of HCLL for a real data set is investigated by using three methods: maximum likelihood, Bayesian and bootstrap (parametric and non-parametric). We evaluate the efficiency of the maximum likelihood estimation method by Monte Carlo simulation.
In addition, in the application section, by using a realistic data set, the superiority of HCLL model to generalized exponential, Weibull, hyperbolic cosine exponential, gamma, weighted exponential distributions is shown through the different criteria of selection model.
