Survival analysis | Probability distributions with non-finite variance | Continuous distributions

Log-logistic distribution

In probability and statistics, the log-logistic distribution (known as the Fisk distribution in economics) is a continuous probability distribution for a non-negative random variable. It is used in survival analysis as a parametric model for events whose rate increases initially and decreases later, as, for example, mortality rate from cancer following diagnosis or treatment. It has also been used in hydrology to model stream flow and precipitation, in economics as a simple model of the distribution of wealth or income, and in networking to model the transmission times of data considering both the network and the software. The log-logistic distribution is the probability distribution of a random variable whose logarithm has a logistic distribution.It is similar in shape to the log-normal distribution but has heavier tails. Unlike the log-normal, its cumulative distribution function can be written in closed form. (Wikipedia).

Log-logistic distribution
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Survival analysis | Censoring (statistics) | Moment (mathematics) | Accelerated failure time model | Shape parameter | Skewness | Statistics | Cumulative frequency analysis | Statistical dispersion | Logarithm | Cumulative distribution function | Probability density function | Probability | Quantile function | Survival function | Weibull distribution | Heavy-tailed distribution | Counting process | Shifted log-logistic distribution | Dagum distribution | Median | Pareto distribution | Quartile | Scale parameter | Log-normal distribution | Variance | Hazard function | Gamma function | Beta prime distribution | List of probability distributions | Mortality rate | Beta function | Parametric model | Random variable | Expected value | Binomial distribution | Kurtosis | Metalog distribution | Logistic distribution