LogLogisticDistribution Class

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, for example mortality rate from cancer following diagnosis or treatment. It has also been used in hydrology to model stream flow and precipitation, and in economics as a simple model of the distribution of wealth or income.

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. Its cumulative distribution function can be written in closed form, unlike that of the log-normal.

References:

• Wikipedia, The Free Encyclopedia. Log-logistic distribution. Available on: http://en.wikipedia.org/wiki/Log-logistic_distribution

This examples shows how to create a Log-Logistic distribution and compute some of its properties and characteristics.

// Create a LLD2 distribution with scale = 0.42, shape = 2.2
var log = new LogLogisticDistribution(scale: 0.42, shape: 2.2);

double mean = log.Mean;     // 0.60592605102976937
double median = log.Median; // 0.42
double mode = log.Mode;     // 0.26892249963239817
double var = log.Variance;  // 1.4357858982592435

double cdf = log.DistributionFunction(x: 1.4);           // 0.93393329906725353
double pdf = log.ProbabilityDensityFunction(x: 1.4);     // 0.096960115938100763
double lpdf = log.LogProbabilityDensityFunction(x: 1.4); // -2.3334555609306102

double ccdf = log.ComplementaryDistributionFunction(x: 1.4); // 0.066066700932746525
double icdf = log.InverseDistributionFunction(p: cdf);       // 1.4000000000000006

double hf = log.HazardFunction(x: 1.4);            // 1.4676094699628273
double chf = log.CumulativeHazardFunction(x: 1.4); // 2.7170904270953637

string str = log.ToString(CultureInfo.InvariantCulture); // LogLogistic(x; α = 0.42, β = 2.2)

Reference