Marshall-Olkin Generalized Inverse Log-Logistic Distribution: Its properties and applications

Abstract

Marshall-Olkin G method of generalization is used to develop a new distribution named Marshall-Olkin Inverse log-logistic distribution (MOILLD), which has a more tractable form and can cope well with outliers in the upper tails. The statistical properties of the distribution, such as survival function, hazard function, moments, and order statistic, were investigated. The mean, variance, and mode of the distribution were also derived. The maximum likelihood estimation method was used to estimates the parameters of the distribution. The result of real-life data application showed that MOILLD has the least AIC, BIC, negative log-likelihood, and KS
values compared with its competing distributions. Hence, an excellent alternative to Inverse log-logistic, Weibull, and log-normal distributions.