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The Logistic Distribution
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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 themean of the distribution, and a scale parameter. The
probability density function is:
The logistic distribution is implemented by the LogisticDistribution
class. It has one constructor with two parameters. The first
parameter is the location parameter, and corresponds to the mode of
the probability density function. The second parameter is the scale
parameter.
The following constructs the same logistic distribution with
location parameter 6.8 and scale parameter 4.1:
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LogisticDistribution logistic = new LogisticDistribution(6.8, 4.1); |
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Dim logistic As LogisticDistribution = 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,
GetRandomVariate, which generates a random variate
using a user-supplied uniform random number generator. The second
and third parameters are the location and scale parameters of the
distribution.
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MersenneTwister random = new MersenneTwister();
double variate = LogisticDistribution.GetRandomVariate(random, 6.8, 4.1); |
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Dim random As MersenneTwister = New MersenneTwister()
Dim variate As Double = LogisticDistribution.GetRandomVariate(random, 6.8, 4.1) |
The above example uses the Mersenne
Twister to generate uniform random numbers.
For details of the properties and methods common to all
continuous distribution classes, see the topic on ContinuousDistribution
class.
Up: Continuous Probability Distributions Next: The Lognormal Distribution Previous: The Laplace Distribution Contents
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