Class EmpiricalDistribution
- java.lang.Object
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- dev.nm.stat.distribution.univariate.EmpiricalDistribution
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- All Implemented Interfaces:
ProbabilityDistribution
- Direct Known Subclasses:
ADFAsymptoticDistribution,ADFAsymptoticDistribution1,ADFDistribution,ADFFiniteSampleDistribution,FisherExactDistribution,JarqueBeraDistribution,JohansenAsymptoticDistribution
public class EmpiricalDistribution extends Object implements ProbabilityDistribution
An empirical cumulative probability distribution function is a cumulative probability distribution function that assigns probability 1/n at each of the n numbers in a sample. The R equivalent function isecdf.
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Constructor Summary
Constructors Constructor Description EmpiricalDistribution(double[] data)Construct an empirical distribution from a sample using the default quantile typeQuantile.QuantileType.APPROXIMATELY_MEDIAN_UNBIASED.EmpiricalDistribution(double[] observations, Quantile.QuantileType quantileType)Construct an empirical distribution from a sample.
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Method Summary
All Methods Instance Methods Concrete Methods Deprecated Methods Modifier and Type Method Description doublecdf(double x)Gets the cumulative probability F(x) = Pr(X ≤ x).doubledensity(double x)This is the probability mass function for the discrete sample.doubleentropy()Deprecated.Not supported yet.doublekurtosis()Gets the excess kurtosis of this distribution.doublemean()Gets the mean of this distribution.doublemedian()Gets the median of this distribution.doublemoment(double x)Deprecated.Not supported yet.intnSamples()Get the number of samples in the empirical distribution.doublequantile(double u)Gets the quantile, the inverse of the cumulative distribution function.doubleskew()Gets the skewness of this distribution.double[]toArray()Get the sorted sample.doublevariance()Gets the variance of this distribution.
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Constructor Detail
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EmpiricalDistribution
public EmpiricalDistribution(double[] observations, Quantile.QuantileType quantileType)Construct an empirical distribution from a sample.- Parameters:
observations- a samplequantileType- specify how the quantile function is computed
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EmpiricalDistribution
public EmpiricalDistribution(double[] data)
Construct an empirical distribution from a sample using the default quantile typeQuantile.QuantileType.APPROXIMATELY_MEDIAN_UNBIASED.- Parameters:
data- a sample
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Method Detail
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nSamples
public int nSamples()
Get the number of samples in the empirical distribution.- Returns:
- the number of samples
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toArray
public double[] toArray()
Get the sorted sample.- Returns:
- the sorted sample
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mean
public double mean()
Description copied from interface:ProbabilityDistributionGets the mean of this distribution.- Specified by:
meanin interfaceProbabilityDistribution- Returns:
- the mean
- See Also:
- Wikipedia: Expected value
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median
public double median()
Description copied from interface:ProbabilityDistributionGets the median of this distribution.- Specified by:
medianin interfaceProbabilityDistribution- Returns:
- the median
- See Also:
- Wikipedia: Median
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variance
public double variance()
Description copied from interface:ProbabilityDistributionGets the variance of this distribution.- Specified by:
variancein interfaceProbabilityDistribution- Returns:
- the variance
- See Also:
- Wikipedia: Variance
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skew
public double skew()
Description copied from interface:ProbabilityDistributionGets the skewness of this distribution.- Specified by:
skewin interfaceProbabilityDistribution- Returns:
- the skewness
- See Also:
- Wikipedia: Skewness
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kurtosis
public double kurtosis()
Description copied from interface:ProbabilityDistributionGets the excess kurtosis of this distribution.- Specified by:
kurtosisin interfaceProbabilityDistribution- Returns:
- the excess kurtosis
- See Also:
- Wikipedia: Kurtosis
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entropy
@Deprecated public double entropy()
Deprecated.Not supported yet.Description copied from interface:ProbabilityDistributionGets the entropy of this distribution.- Specified by:
entropyin interfaceProbabilityDistribution- Returns:
- the entropy
- See Also:
- Wikipedia: Entropy (information theory)
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cdf
public double cdf(double x)
Description copied from interface:ProbabilityDistributionGets the cumulative probability F(x) = Pr(X ≤ x).- Specified by:
cdfin interfaceProbabilityDistribution- Parameters:
x- x- Returns:
- F(x) = Pr(X ≤ x)
- See Also:
- Wikipedia: Cumulative distribution function
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quantile
public double quantile(double u)
Gets the quantile, the inverse of the cumulative distribution function. It is the value below which random draws from the distribution would fall u×100 percent of the time.
This may not always exist. For an empirical distribution, this implementation assumes the following.F-1(u) = x, such that Pr(X ≤ x) = u
F-1(0) = the minimum x value F-1(1) = the maximum x value
- Specified by:
quantilein interfaceProbabilityDistribution- Parameters:
u-u, a quantile- Returns:
- F-1(u)
- See Also:
- Wikipedia: Quantile function
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density
public double density(double x)
This is the probability mass function for the discrete sample.- Specified by:
densityin interfaceProbabilityDistribution- Parameters:
x- an observation- Returns:
pmf(x)- See Also:
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moment
@Deprecated public double moment(double x)
Deprecated.Not supported yet.Description copied from interface:ProbabilityDistributionThe moment generating function is the expected value of etX. That is,E(etX)
This may not always exist.- Specified by:
momentin interfaceProbabilityDistribution- Parameters:
x- t- Returns:
- E(exp(tX))
- See Also:
- Wikipedia: Moment-generating function
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