public class OrderStatisticsDistribution extends Object implements UnivariateEVD
evd::dorder
, evd::porder
, evd::rorder
.Constructor and Description |
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OrderStatisticsDistribution(ProbabilityDistribution dist,
int nIIDs,
int order)
Create an instance with the probability distribution of \(X\), the number of iid samples
to be drawn, and the order statistic.
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Modifier and Type | Method and Description |
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double |
cdf(double x)
Gets the cumulative probability F(x) = Pr(X ≤ x).
|
double |
density(double x)
The density function, which, if exists, is the derivative of F.
|
double |
entropy()
Gets the entropy of this distribution.
|
double |
kurtosis()
Gets the excess kurtosis of this distribution.
|
double |
logDensity(double x)
Get the logarithm of the probability density function at \(x\), that is, \(\log(f(x))\).
|
double |
mean()
Gets the mean of this distribution.
|
double |
median()
Gets the median of this distribution.
|
double |
moment(double x)
The moment generating function is the expected value of etX.
|
double |
quantile(double x)
Gets the quantile, the inverse of the cumulative distribution function.
|
double |
skew()
Gets the skewness of this distribution.
|
double |
variance()
Gets the variance of this distribution.
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public OrderStatisticsDistribution(ProbabilityDistribution dist, int nIIDs, int order)
dist
- the probability distributionnIIDs
- the number of independent variablesorder
- the order statistic (largest) (1 means smallest, n means largest)public double density(double x)
ProbabilityDistribution
f(x) = dF(X) / dxThis may not always exist. For the discrete cases, this is the probability mass function. It gives the probability that a discrete random variable is exactly equal to some value.
density
in interface ProbabilityDistribution
x
- xpublic double logDensity(double x)
UnivariateEVD
logDensity
in interface UnivariateEVD
x
- \(x\)public double cdf(double x)
ProbabilityDistribution
cdf
in interface ProbabilityDistribution
x
- xpublic double quantile(double x)
ProbabilityDistribution
This may not always exist.F-1(u) = x, such that Pr(X ≤ x) = u
quantile
in interface ProbabilityDistribution
x
- u
, a quantilepublic double mean()
ProbabilityDistribution
mean
in interface ProbabilityDistribution
public double moment(double x)
ProbabilityDistribution
E(etX)This may not always exist.
moment
in interface ProbabilityDistribution
x
- tpublic double skew()
ProbabilityDistribution
skew
in interface ProbabilityDistribution
public double variance()
ProbabilityDistribution
variance
in interface ProbabilityDistribution
public double median()
ProbabilityDistribution
median
in interface ProbabilityDistribution
public double kurtosis()
ProbabilityDistribution
kurtosis
in interface ProbabilityDistribution
public double entropy()
ProbabilityDistribution
entropy
in interface ProbabilityDistribution
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