Abstract
In this paper, we present a review on the log-logistic distribution and some of its recent generalizations. We cite more than twenty distributions obtained by different generating families of univariate continuous distributions or compounding methods on the log-logistic distribution. We reviewed some log-logistic mathematical properties, including the eight different functions used to define lifetime distributions. These results were used to obtain the properties of some log-logistic generalizations from linear representations. A real-life data application is presented to compare some of the surveyed distributions.
Highlights
The log-logistic distribution, known as Fisk distribution in economics, is one of the important continuous probability distributions with a heavy tail defined by one scale and one shape parameters
Khan and Khosa (2015) proposed a generalized log-logistic distribution that belongs to the Proportional hazard (PH) family and they described that it has properties identical to those of log-logistic, and tend to the Weibull in the limit, and they defined that these features enable the model to handle all kinds of hazard functions
We review some of the statistical and mathematical properties of the LL distribution
Summary
The log-logistic distribution, known as Fisk distribution in economics, is one of the important continuous probability distributions with a heavy tail defined by one scale (or one rate) and one shape parameters.
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