The log‐logistic distribution (LLD) is very useful in a wide variety of applications, especially in the analysis of survival data (O'Quigley and Struthers 1982; Bennett 1983; Cox and Snell 1989). The LLD is very similar in shape to the log‐normal distribution, however it has the advantage of having simple algebraic expressions for its survivor and hazard functions and a closed form for its distribution function. It is therefore more convenient than the log‐normal distribution in handling censored data. However, due to the symmetry of the log‐logistic distribution, it may be inappropriate for modelling censored survival date, especially for the cases where the hazard rate is skewed or heavily tailed. In this article we present a generalization of the LLD and refer to this as the generalized log‐logistic distribution (GLLD). The suggested GLLD reflects the skewness and the structure of the heavy tail and generally shows some improvement over the LLD. In addition, we generalize a result characterizing the log‐logistic distribution given by Shoukri, Mian, and Tracy (1988) and introduce two characterization theorems of the GLLD. Copyright © 1990 John Wiley & Sons, Ltd
