Contents
- Index
Loglogistic Family of Distributions
Shape:
The loglogistic family of distributions is made up of three distributions: loglogistic, negative loglogistic and logistic. It covers any specified average, standard deviation and any skewness in the range of -4.2847830295411833030 to 4.2847830295411833030. Together they form a 3-parameter family of distributions that is represented by a curve on a skewness-kurtosis plot as shown below. The loglogistic distribution covers the positive skewness portion of the curve. The negative loglogistic distribution covers the negative skewness portion of the curve. The logistic distribution handles the remaining case of zero skewness.
Density Function - Logistic:
The density function of the logistic distribution is shown below:
The equation, parameters and bounds of the density function are:
Moments - Logistic:
The moments of the logistic distribution can be calculated from the parameters as shown below:
Density Function - Loglogistic:
The density function of the loglogistic distribution is shown below:
The equation, parameters and bounds of the density function are:
Moments - Loglogistic:
The moments of the loglogistic distribution can be calculated from the parameters as shown below:
Properties:
Commonly used in growth models.