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Unit Log-Logistic Distribution and Unit Log-Logistic Regression Model


In this paper, the unit log-logistic distribution was proposed. This distribution is obtained through by transformation of a random variable with log-logistic distribution. The unit log-logistic has closed forms for the cumulative distribution function and quantile function. Subsequently, the unit log-logistic regression model, with parametrization in the median was defined. So, in the presence of outliers, this model is more robust than the models with parametrization in the mean. The maximum likelihood method was used to estimate the parameters. The validity of the estimators of this model is shown through Monte Carlo simulations. Application to real data showed that the new model has a better fit than the popular beta regression model.

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  1. The betareg package can be installed with install.packages(”betareg”) command.


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Correspondence to Lucas David Ribeiro-Reis.

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Ribeiro-Reis, L.D. Unit Log-Logistic Distribution and Unit Log-Logistic Regression Model. J Indian Soc Probab Stat 22, 375–388 (2021).

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  • Unit log-logistic distribution
  • Unit log-logistic regression model
  • Median
  • Quantile function
  • Outliers

Mathematics Subject Classification

  • 60E05
  • 62F12
  • 65C05
  • 65C10