Package smile.stat.distribution
Class LogisticDistribution
java.lang.Object
smile.stat.distribution.AbstractDistribution
smile.stat.distribution.LogisticDistribution
- All Implemented Interfaces:
Serializable
,Distribution
The logistic distribution is a continuous probability distribution whose
cumulative distribution function is the logistic function, which appears
in logistic regression and feedforward neural networks. It resembles
the normal distribution in shape but has heavier tails (higher kurtosis).
The logistic distribution and the S-shaped pattern that results from it have been extensively used in many different areas such as:
- Biology - to describe how species populations grow in competition.
- Epidemiology - to describe the spreading of epidemics.
- Psychology - to describe learning.
- Technology - to describe how new technologies diffuse and substitute for each other.
- Market - the diffusion of new-product sales.
- Energy - the diffusion and substitution of primary energy sources.
- See Also:
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Field Summary
Fields -
Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptiondouble
cdf
(double x) Cumulative distribution function.double
entropy()
Shannon entropy of the distribution.int
length()
The number of parameters of the distribution.double
logp
(double x) The density at x in log scale, which may prevents the underflow problem.double
mean()
The mean of distribution.double
p
(double x) The probability density function for continuous distribution or probability mass function for discrete distribution at x.double
quantile
(double p) The quantile, the probability to the left of quantile is p.double
rand()
Generates a random number following this distribution.double
sd()
The standard deviation of distribution.toString()
double
variance()
The variance of distribution.Methods inherited from class smile.stat.distribution.AbstractDistribution
inverseTransformSampling, quantile, quantile, rejection
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
Methods inherited from interface smile.stat.distribution.Distribution
likelihood, logLikelihood, rand
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Field Details
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mu
public final double muThe location parameter. -
scale
public final double scaleThe scale parameter.
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Constructor Details
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LogisticDistribution
public LogisticDistribution(double mu, double scale) Constructor.- Parameters:
mu
- the location parameter.scale
- the scale parameter.
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Method Details
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length
public int length()Description copied from interface:Distribution
The number of parameters of the distribution. The "length" is in the sense of the minimum description length principle.- Returns:
- The number of parameters.
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mean
public double mean()Description copied from interface:Distribution
The mean of distribution.- Returns:
- The mean.
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variance
public double variance()Description copied from interface:Distribution
The variance of distribution.- Returns:
- The variance.
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sd
public double sd()Description copied from interface:Distribution
The standard deviation of distribution.- Returns:
- The standard deviation.
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entropy
public double entropy()Description copied from interface:Distribution
Shannon entropy of the distribution.- Returns:
- Shannon entropy.
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toString
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rand
public double rand()Description copied from interface:Distribution
Generates a random number following this distribution.- Returns:
- a random number.
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p
public double p(double x) Description copied from interface:Distribution
The probability density function for continuous distribution or probability mass function for discrete distribution at x.- Parameters:
x
- a real number.- Returns:
- the density.
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logp
public double logp(double x) Description copied from interface:Distribution
The density at x in log scale, which may prevents the underflow problem.- Parameters:
x
- a real number.- Returns:
- the log density.
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cdf
public double cdf(double x) Description copied from interface:Distribution
Cumulative distribution function. That is the probability to the left of x.- Parameters:
x
- a real number.- Returns:
- the probability.
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quantile
public double quantile(double p) Description copied from interface:Distribution
The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.- Parameters:
p
- the probability.- Returns:
- the quantile.
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