The Logistic Distribution

The logistic distribution can be used to model growth. In many processes, the growth is slow at the beginning, picks up in the middle, and slows down again when approaching a saturation point. Examples of applications of the logistic distribution are:

  • Population growth.

  • Market share of a new product.

The logistic distribution has a location parameter corresponding to the mean of the distribution, and a scale parameter. The probability density function is:

Probability density of the logistic distribution.

The logistic distribution is implemented by the LogisticDistribution class. It has one constructor that takes two argument. The first argument is the location parameter, and corresponds to the mode of the probability density function. The second argument is the scale parameter.

The following constructs the same logistic distribution with location parameter 6.8 and scale parameter 4.1:

var logistic = new LogisticDistribution(6.8, 4.1);

The LogisticDistribution class has two specific properties, LocationParameter and ScaleParameter, which return the location parameter (mode) and scale parameter of the distribution.

LogisticDistribution has one static (Shared in Visual Basic) method, Sample, which generates a random sample using a user-supplied uniform random number generator. The second and third parameters are the location and scale parameters of the distribution.

var random = new MersenneTwister();
double sample = LogisticDistribution.Sample(random, 6.8, 4.1);

The above example uses the MersenneTwister class to generate uniform random numbers.

For details of the properties and methods common to all continuous distribution classes, see the topic on continuous distributions..