‎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.