In this paper, a new probability distribution based on the family of hyperbolic cosine F-(HCF) distributions is introduced and its various statistical properties and reliability are investigated. The new class of HCF distributions is obtained by combining a cumulative F distribution with the hyperbolic cosine function. Based on the basic log-logistic distribution, a new distribution called hyperbolic cosine log-logistic (HCLL) is introduced and various properties of the distribution such as moments, quantiles, moment generating function, failure rate function, mean remaining life, ordinal statistics and stress-resistance parameter are presented. The estimation of the parameters of the HCLL distribution for a real data set is investigated through three methods: maximum likelihood, Bayesian and autocorrelation (parametric and nonparametric). The efficiency of the maximum likelihood estimation method is evaluated through Monte Carlo simulation. Also, in the application section, using a real dataset, the superiority of the HCLL model over the generalized exponential, Weibull, exponential hyperbolic cosine, gamma, and weighted exponential distributions is demonstrated through various model selection criteria.