On parameter estimation of the standard omega distribution

The standard omega distribution is defined on the unit interval so that it is a probabilistic model for observations in rates and percentages. It is, in fact, the unit form of the exponentiated half logistic distribution. In this work, we first give a detailed shape analysis from which we observe that it is another flexible beta-like distribution. We observe that it can be J-shaped, reverse J-shaped, U-shaped, unimodal and show left and right skewness according to the values of its shape parameters. Contrary to the ordinary beta, it has the advantage of having a clear distribution function. We then discuss the existence and uniqueness of the maximum likelihood estimators and the Bayesian estimate of the parameters. The existence and uniqueness of the maximum likelihood estimators of the parameters will give a great advantage to the possible practitioners of this model since the possibility of finding a spurious solution to the likelihood equations disappears then. The comparison of these estimators with the existing ones for the general omega distribution is made with the help of a simulation study. Two real data fitting demonstrations prove its usefulness among other beta-like distributions such as Kumaraswamy, log-Lindley and Topp-Leone.