java.lang.Object

org.sm.smtools.math.statistics.EmpiricalDistribution

public final class EmpiricalDistribution
extends java.lang.Object

The EmpiricalDistribution class offers a means to calculate the empirical cumulative distribution (CDF) and probability density (PDF) functions, including percentiles. After the distribution is created, a user will typically call the analyse() method to estimate the various statistical quantities.

The distribution can only contain Integer.MAX_VALUE samples.

Note that a valid I18NL10N database must be available!

Note that this class cannot be subclassed!

Version:: 26/06/2018
Author:: Sven Maerivoet

Constructor Summary

Constructors
Constructor	Description
`EmpiricalDistribution()`	Constructs an empty `EmpiricalDistribution` object.
`EmpiricalDistribution(double[] x)`	Constructs an `EmpiricalDistribution` object for a given array of values.
`EmpiricalDistribution(double[] x, double[] histogramBinRightEdges)`	Constructs an `EmpiricalDistribution` object for a given array of values and user-specified histogram bin right edges.
`EmpiricalDistribution(double[] x, int nrOfHistogramBins)`	Constructs an `EmpiricalDistribution` object for a given array of values and a user-specified number of histogram bins.

Method Summary

Modifier and Type	Method	Description
`void`	`analyse()`	Estimates the empirical distribution and analyses it various statistical quantities.
`double`	`calculateKDEPDFBandwidth(MathTools.EKernelType kernelType)`	Calculates the bandwidth for kernel density estimation (KDE) based on Silverman's Rule-of-Thumb.
`void`	`clear()`	Clears the empirical distribution.
`void`	`estimateKDEPDF(MathTools.EKernelType kernelType, double bandwidth, int nrOfSupportPoints, double minSupport, double maxSupport)`	Estimates the probability distribution function (PDF) using a specified kernel function.
`double`	`getCDF(double x)`	Returns the value of the cumulative distribution function (CDF) evaluated at `x`.
`static double`	`getChiSquare(double alpha, int degreesOfFreedom)`	Returns the chi-square value corresponding to a specified alpha level and number of degrees of freedom.
`double[]`	`getData()`	Retrieves the raw data for this empirical distribution.
`double`	`getExpectedValue()`	Returns the expected value for the first moment (population mean), which in this case is approximated by the sample mean.
`FunctionLookupTable`	`getFullKDEPDF()`	Returns the previously complete calculated kernel density estimation (KDE) of the probability distribution function (PDF).
`double`	`getHistogramBinCentre(int histogramBin)`	Returns the centre of a specified histogram bin.
`double[]`	`getHistogramBinCentres()`	Returns the centres of all the histogram bins.
`double`	`getHistogramBinCount(int histogramBin)`	Returns the count associated with a specified histogram bin.
`double[]`	`getHistogramBinCounts()`	Returns the counts for all the histogram bins.
`double[]`	`getHistogramBinFrequencies()`	Returns the frequencies for all the histogram bins.
`double`	`getHistogramBinFrequency(int histogramBin)`	Returns the frequency associated with a specified histogram bin.
`double`	`getHistogramBinWidth()`	Returns the width of a histogram bin.
`double`	`getInterquartileRange()`	Returns the interquartile range (IQR) (i.e., the difference between the 75th and the 25th percentiles).
`static java.lang.String`	`getInterquartileRangeDescription()`	Returns a descriptive label of the interquartile range (IQR).
`double`	`getJarqueBeraTestStatistic()`	Calculates the Jarque-Bera test statistic.
`double`	`getKDEPDF(double x)`	Returns the value of the probability density function (PDF) evaluated at `x` (based on kernel density estimation, KDE).
`FunctionLookupTable`	`getKDEPDFModes()`	Returns all modes (i.e., local maxima) for the calculated kernel density estimation (KDE) of the probability density function (PDF).
`double`	`getKDEXMaximum()`	Returns the maximum of the values for a kernel density estimation (KDE) of the probability distribution function (PDF).
`double`	`getKDEXMinimum()`	Returns the minimum of the values for a kernel density estimation (KDE) of the probability distribution function (PDF).
`double`	`getKDEXRange()`	Returns the range of the values for a kernel density estimation (KDE) of the probability distribution function (PDF).
`double`	`getKurtosis()`	Returns the sample kurtosis (using an unbiased estimator).
`static java.lang.String`	`getKurtosisDescription()`	Returns a descriptive label of the kurtosis.
`java.lang.String`	`getKurtosisInterpretation()`	Returns a qualitative description of the kurtosis based on its test statistic.
`double`	`getKurtosisZStatistic()`	Returns a two-tailed test statistic Z of kurtosis (different from zero) with a 5% significance level.
`double`	`getMean()`	This is the sample mean, which in this case is an alias for the expected value.
`static java.lang.String`	`getMeanDescription()`	Returns a descriptive label of the mean (expected value).
`double`	`getMedian()`	Returns the median (i.e., the 50th percentile).
`static java.lang.String`	`getMedianDescription()`	Returns a descriptive label of the median.
`int`	`getN()`	Returns the sample size.
`int`	`getNrOfHistogramBins()`	Returns the number of histogram bins used for estimating the probability density function (PDF).
`boolean[]`	`getOutliers()`	Returns the outliers which are defined as having z-scores greater than 3.
`double`	`getPDF(double x)`	Returns the value of the probability density function (PDF) evaluated at `x` (based on a histogram).
`double`	`getPercentile(double percentile)`	Returns the given percentile.
`double`	`getPercentile(int percentile)`	Returns the given percentile.
`static java.lang.String`	`getPercentileDescription()`	Returns a descriptive label of a percentile.
`double[]`	`getPercentiles()`	Returns all the percentiles for the range [0,100].
`double`	`getSkewness()`	Returns the sample skewness (using an unbiased estimator).
`double`	`getSkewnessConfidenceBounds()`	Returns the symmetrical skewness' confidence bounds for a 95% confidence interval, defined as twice the standard error of skewness (SES).
`static java.lang.String`	`getSkewnessDescription()`	Returns a descriptive label of the skewness.
`java.lang.String`	`getSkewnessInterpretation()`	Returns a qualitative description of the skewness based on its test statistic.
`double`	`getSkewnessZStatistic()`	Returns a two-tailed test statistic Z of skewness (different from zero) with a 5% significance level.
`double[]`	`getSortedData()`	Retrieves the raw data for this empirical distribution.
`double`	`getStandardDeviation()`	Returns the standard deviation (i.e., the positive square root of the variance).
`static java.lang.String`	`getStandardDeviationDescription()`	Returns a descriptive label of the standard deviation.
`double`	`getTrimmedMean(double percentageToTrim)`	This is the trimmed (or truncated) mean, which corresponds to the mean calculated after symmetrically discarding a certain percentage of data points at the high and low end (without interpolation).
`double`	`getVariance()`	Returns the sample variance (using an unbiased estimator of the population variance).
`static java.lang.String`	`getVarianceDescription()`	Returns a descriptive label of the variance.
`double`	`getXMaximum()`	Returns the maximum of the input values.
`double`	`getXMinimum()`	Returns the minimum of the input values.
`double`	`getXRange()`	Returns the range of the input values.
`double[]`	`getZScores()`	Returns the calculated z-scores, defined as:
`boolean`	`isJarqueBeraTestAccepted(double alpha)`	Compares the Jarque-Bera test statistic with the chi-square distribution with 2 degrees of freedom for a given alpha level.
`void`	`recalculatePDF()`	Recalculates the probability density function (PDF).
`void`	`recalculatePDF(int nrOfHistogramBins)`	Recalculates the probability density function (PDF) using a user-specified number of histogram bins.
`void`	`setData(double[] x)`	Sets the source data for the empirical distribution.
`void`	`setData(double[] x, int nrOfHistogramBins)`	Sets the source data for the empirical distribution, as well as a user-specified number of histogram bins.

Methods inherited from class java.lang.Object

clone, equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details
- EmpiricalDistribution
  
  public EmpiricalDistribution()
  
  Constructs an empty EmpiricalDistribution object.
- EmpiricalDistribution
  
  public EmpiricalDistribution(double[] x)
  
  Constructs an EmpiricalDistribution object for a given array of values.
  The Freedman-Diaconis rule is applied for finding the optimal histogram bin width, and consequently the optimal number of histogram bins:
  bin width = 2 * IQR / n^1/3
  
  Parameters:
  
  x - the array of values to estimate the empirical distribution for
- EmpiricalDistribution
  
  public EmpiricalDistribution(double[] x, int nrOfHistogramBins)
  
  Constructs an EmpiricalDistribution object for a given array of values and a user-specified number of histogram bins.
  
  Parameters:
  
  x - the array of values to estimate the empirical distribution for
  
  nrOfHistogramBins - the user-specified number of histogram bins
- EmpiricalDistribution
  
  public EmpiricalDistribution(double[] x, double[] histogramBinRightEdges)
  
  Constructs an EmpiricalDistribution object for a given array of values and user-specified histogram bin right edges.
  
  Parameters:
  
  x - the array of values to estimate the empirical distribution for
  
  histogramBinRightEdges - the array of values containing the histogram bin right edges
Method Details
- getData
  
  public double[] getData()
  
  Retrieves the raw data for this empirical distribution.
  
  Returns:
  
  the raw data for this empirical distribution
  
  See Also:
  
  getSortedData()
- getSortedData
  
  public double[] getSortedData()
  
  Retrieves the raw data for this empirical distribution.
  
  Returns:
  
  the raw data for this empirical distribution
  
  See Also:
  
  getData()
- setData
  
  public void setData(double[] x)
  
  Sets the source data for the empirical distribution.
  The Freedman-Diaconis rule is applied for finding the optimal histogram bin width, and consequently the optimal number of histogram bins:
  bin width = 2 * IQR / n^1/3
  
  Parameters:
  
  x - the array of values to estimate the empirical distribution for
- setData
  
  public void setData(double[] x, int nrOfHistogramBins)
  
  Sets the source data for the empirical distribution, as well as a user-specified number of histogram bins.
  
  Parameters:
  
  x - the array of values to estimate the empirical distribution for
  
  nrOfHistogramBins - the user-specified number of histogram bins
- clear
  
  public void clear()
  
  Clears the empirical distribution.
- analyse
  
  public void analyse()
  
  Estimates the empirical distribution and analyses it various statistical quantities.
- getCDF
  
  public double getCDF(double x)
  
  Returns the value of the cumulative distribution function (CDF) evaluated at x.
  
  Parameters:
  
  x - the value to evaluate the cumulative distribution function at
  
  Returns:
  
  the value of the cumulative distribution function evaluated at x
- getPercentile
  
  public double getPercentile(int percentile)
  
  Returns the given percentile.
  
  Parameters:
  
  percentile - the requested percentile (in the interval [0,100])
  
  Returns:
  
  the requested percentile value
- getPercentile
  
  public double getPercentile(double percentile)
  
  Returns the given percentile.
  
  Parameters:
  
  percentile - the requested percentile (in the interval [0.0,100.0])
  
  Returns:
  
  the requested percentile value
- getPercentiles
  
  public double[] getPercentiles()
  
  Returns all the percentiles for the range [0,100].
  
  Returns:
  
  an array containing all the percentiles in the range [0,100]
- getXMinimum
  
  public double getXMinimum()
  
  Returns the minimum of the input values.
  
  Returns:
  
  the minimum of the input values
- getXMaximum
  
  public double getXMaximum()
  
  Returns the maximum of the input values.
  
  Returns:
  
  the maximum of the input values
- getXRange
  
  public double getXRange()
  
  Returns the range of the input values.
  
  Returns:
  
  the range of the input values
- getKDEXMinimum
  
  public double getKDEXMinimum()
  
  Returns the minimum of the values for a kernel density estimation (KDE) of the probability distribution function (PDF).
  
  Returns:
  
  the minimum of the values for a kernel density estimation (KDE) of the probability distribution function (PDF)
- getKDEXMaximum
  
  public double getKDEXMaximum()
  
  Returns the maximum of the values for a kernel density estimation (KDE) of the probability distribution function (PDF).
  
  Returns:
  
  the maximum of the values for a kernel density estimation (KDE) of the probability distribution function (PDF)
- getKDEXRange
  
  public double getKDEXRange()
  
  Returns the range of the values for a kernel density estimation (KDE) of the probability distribution function (PDF).
  
  Returns:
  
  the range of the values for a kernel density estimation (KDE) of the probability distribution function (PDF)
- getMedian
  
  public double getMedian()
  
  Returns the median (i.e., the 50th percentile).
  
  Returns:
  
  the median
- getInterquartileRange
  
  public double getInterquartileRange()
  
  Returns the interquartile range (IQR) (i.e., the difference between the 75th and the 25th percentiles).
  
  Returns:
  
  the interquartile range (IQR)
- recalculatePDF
  
  public void recalculatePDF()
  
  Recalculates the probability density function (PDF).
  The Freedman-Diaconis rule is applied for finding the optimal histogram bin width, and consequently the optimal number of histogram bins:
  bin width = 2 * IQR / n^1/3
- recalculatePDF
  
  public void recalculatePDF(int nrOfHistogramBins)
  
  Recalculates the probability density function (PDF) using a user-specified number of histogram bins.
  
  Parameters:
  
  nrOfHistogramBins - the user-specified number of histogram bins
- calculateKDEPDFBandwidth
  
  public double calculateKDEPDFBandwidth(MathTools.EKernelType kernelType)
  
  Calculates the bandwidth for kernel density estimation (KDE) based on Silverman's Rule-of-Thumb.
  
  Parameters:
  
  kernelType - the type of kernel function to use in the calculation
  
  Returns:
  
  an estimation of the bandwidth
- estimateKDEPDF
  
  public void estimateKDEPDF(MathTools.EKernelType kernelType, double bandwidth, int nrOfSupportPoints, double minSupport, double maxSupport)
  
  Estimates the probability distribution function (PDF) using a specified kernel function.
  
  Parameters:
  
  kernelType - the type of kernel function to use
  
  bandwidth - the bandwidth of the kernel function
  
  nrOfSupportPoints - the number of (X,Y) values to use for the smoothened 1D function
  
  minSupport - the minimum value for the support
  
  maxSupport - the maximum value for the support
- getNrOfHistogramBins
  
  public int getNrOfHistogramBins()
  
  Returns the number of histogram bins used for estimating the probability density function (PDF).
  
  Returns:
  
  the number of histogram bins used for estimating the probability density function (PDF)
- getHistogramBinCount
  
  public double getHistogramBinCount(int histogramBin)
  
  Returns the count associated with a specified histogram bin.
  
  Parameters:
  
  histogramBin - the histogram bin to lookup the count for
  
  Returns:
  
  the count associated with the specified histogram bin
- getHistogramBinCounts
  
  public double[] getHistogramBinCounts()
  
  Returns the counts for all the histogram bins.
  
  Returns:
  
  an array containing the counts for all the histogram bins
- getHistogramBinFrequency
  
  public double getHistogramBinFrequency(int histogramBin)
  
  Returns the frequency associated with a specified histogram bin.
  
  Parameters:
  
  histogramBin - the histogram bin to lookup the frequency for
  
  Returns:
  
  the frequency associated with the specified histogram bin
- getHistogramBinFrequencies
  
  public double[] getHistogramBinFrequencies()
  
  Returns the frequencies for all the histogram bins.
  
  Returns:
  
  an array containing the frequencies for all the histogram bins
- getHistogramBinCentre
  
  public double getHistogramBinCentre(int histogramBin)
  
  Returns the centre of a specified histogram bin.
  
  Parameters:
  
  histogramBin - the histogram bin to lookup the centre for
  
  Returns:
  
  the centre of the specified histogram bin
- getHistogramBinCentres
  
  public double[] getHistogramBinCentres()
  
  Returns the centres of all the histogram bins.
  
  Returns:
  
  an array containing the centres of all the histogram bins
- getHistogramBinWidth
  
  public double getHistogramBinWidth()
  
  Returns the width of a histogram bin.
  
  Returns:
  
  the width of a histogram bin
- getPDF
  
  public double getPDF(double x)
  
  Returns the value of the probability density function (PDF) evaluated at x (based on a histogram).
  
  Parameters:
  
  x - the value to evaluate the probability density function at
  
  Returns:
  
  the value of the probability density function evaluated at x
- getKDEPDF
  
  public double getKDEPDF(double x)
  
  Returns the value of the probability density function (PDF) evaluated at x (based on kernel density estimation, KDE).
  
  Parameters:
  
  x - the value to evaluate the probability density function at
  
  Returns:
  
  the value of the probability density function evaluated at x
- getFullKDEPDF
  
  public FunctionLookupTable getFullKDEPDF()
  
  Returns the previously complete calculated kernel density estimation (KDE) of the probability distribution function (PDF).
  
  Returns:
  
  the lookup table with X and Y values for the KDE PDF
- getN
  
  public int getN()
  
  Returns the sample size.
  
  Returns:
  
  the sample size
- getExpectedValue
  
  public double getExpectedValue()
  
  Returns the expected value for the first moment (population mean), which in this case is approximated by the sample mean.
  
  Returns:
  
  the expected value for the first moment
  
  See Also:
  
  getMean()
- getMean
  
  public double getMean()
  
  This is the sample mean, which in this case is an alias for the expected value.
  
  Returns:
  
  the sample mean
  
  See Also:
  
  getExpectedValue(), getTrimmedMean(double)
- getTrimmedMean
  
  public double getTrimmedMean(double percentageToTrim)
  
  This is the trimmed (or truncated) mean, which corresponds to the mean calculated after symmetrically discarding a certain percentage of data points at the high and low end (without interpolation).
  
  Parameters:
  
  percentageToTrim - the percentage to trim (left and right combined)
  
  Returns:
  
  the trimmed mean
  
  See Also:
  
  getMean()
- getKDEPDFModes
  
  public FunctionLookupTable getKDEPDFModes()
  
  Returns all modes (i.e., local maxima) for the calculated kernel density estimation (KDE) of the probability density function (PDF).
  
  Returns:
  
  all modes of the specified PDF
- getVariance
  
  public double getVariance()
  
  Returns the sample variance (using an unbiased estimator of the population variance).
  
  Returns:
  
  the sample variance (using an unbiased estimator of the population variance)
- getStandardDeviation
  
  public double getStandardDeviation()
  
  Returns the standard deviation (i.e., the positive square root of the variance).
  
  Returns:
  
  the standard deviation
- getSkewness
  
  public double getSkewness()
  Returns the sample skewness (using an unbiased estimator).
  Skewness implies:
  
  Positive skew: longer right tail, density mass constrained to the left.
  
  Negative skew: longer left tail, density mass constrained to the right.
  
  Note that the amount of skewness is determined as follows:
  
  -0.5 ≤ skewness ≤ +0.5: approximately symmetric distribution.
  
  -1 ≤ skewness < -0.5, or +0.5 < skewness ≤ +1: moderately skewed distribution.
  
  skewness < -1, or skewness > +1: highly skewed distribution.
  Returns:
  
  the sample skewness (using an unbiased estimator)
- getSkewnessConfidenceBounds
  
  public double getSkewnessConfidenceBounds()
  
  Returns the symmetrical skewness' confidence bounds for a 95% confidence interval, defined as twice the standard error of skewness (SES).
  
  Returns:
  
  the symmetrical skewness' confidence bounds for a 95% confidence interval
- getSkewnessZStatistic
  
  public double getSkewnessZStatistic()
  Returns a two-tailed test statistic Z of skewness (different from zero) with a 5% significance level.
  
  Z > +2: population is very likely positively skewed.
  
  Z < -2: population is very likely negatively skewed.
  
  -2 ≤ Z ≤ +2: inconclusive (might be symmetric, might be skewed).
  
  The larger Z, the higher the probability.
  Returns:
  
  the skewness Z-statistic
- getKurtosis
  
  public double getKurtosis()
  Returns the sample kurtosis (using an unbiased estimator).
  The value returned is the excess kurtosis, such that it is zero for a normal distribution:
  
  Mesokurtic: has zero excess (e.g., normal distribution).
  
  Leptokurtic: has positive excess, higher and sharper central peak, with longer and fatter tails (i.e., more extreme values).
  
  Platykurtic: has negative excess, lower and broader central peak, with shorter and thinner tails (i.e., less extreme values).
  
  As the kurtosis increases, more probability mass is transferred from the distribution's shoulders to the centre and tails.
  Returns:
  
  the sample kurtosis (using an unbiased estimator)
- getKurtosisZStatistic
  
  public double getKurtosisZStatistic()
  Returns a two-tailed test statistic Z of kurtosis (different from zero) with a 5% significance level.
  
  Z > +2: population has very likely positive kurtosis (leptokurtic).
  
  Z < -2: population has very likely negative kurtosis (platykurtic).
  
  -2 ≤ Z ≤ +2: inconclusive (might be negative, zero, or positive kurtosis).
  
  The larger Z, the higher the probability.
  Returns:
  
  the kurtosis Z-statistic
- getJarqueBeraTestStatistic
  
  public double getJarqueBeraTestStatistic()
  
  Calculates the Jarque-Bera test statistic.
  This tests the goodness-of-fit of whether the distribution's skewness and kurtosis match that of the normal distribution.
  The test result should be compared to the values of the chi-square distribution with 2 degrees of freedom.
  
  Returns:
  
  the Jarque-Bera test statistic
  
  See Also:
  
  isJarqueBeraTestAccepted(double), getChiSquare(double,int)
- isJarqueBeraTestAccepted
  
  public boolean isJarqueBeraTestAccepted(double alpha)
  
  Compares the Jarque-Bera test statistic with the chi-square distribution with 2 degrees of freedom for a given alpha level.
  Alpha levels can be 0.995, 0.99, 0.975, 0.95, 0.90, 0.10, 0.05, 0.025, 0.01, or 0.005.
  
  Parameters:
  
  alpha - the alpha level
  
  Returns:
  
  true if the test is accepted, false if it is rejected
  
  See Also:
  
  getJarqueBeraTestStatistic(), getChiSquare(double,int)
- getChiSquare
  
  public static double getChiSquare(double alpha, int degreesOfFreedom)
  
  Returns the chi-square value corresponding to a specified alpha level and number of degrees of freedom.
  Alpha levels can be 0.995, 0.99, 0.975, 0.95, 0.90, 0.10, 0.05, 0.025, 0.01, or 0.005.
  The number of degrees of freedom is clipped between 1 and 100.
  
  Parameters:
  
  alpha - the alpha level
  
  degreesOfFreedom - the number of degrees of freedom
  
  Returns:
  
  the chi-square value corresponding to the specified alpha level and number of degrees of freedom
  
  See Also:
  
  getJarqueBeraTestStatistic(), isJarqueBeraTestAccepted(double)
- getZScores
  
  public double[] getZScores()
  
  Returns the calculated z-scores, defined as:
  (value - mean) / standard deviation
  
  Returns:
  
  the z-scores
  
  See Also:
  
  getOutliers()
- getOutliers
  
  public boolean[] getOutliers()
  
  Returns the outliers which are defined as having z-scores greater than 3.
  
  Returns:
  
  the outliers
  
  See Also:
  
  getZScores()
- getMeanDescription
  
  public static java.lang.String getMeanDescription()
  
  Returns a descriptive label of the mean (expected value).
  
  Returns:
  
  a descriptive label of the mean
- getStandardDeviationDescription
  
  public static java.lang.String getStandardDeviationDescription()
  
  Returns a descriptive label of the standard deviation.
  
  Returns:
  
  a descriptive label of the standard deviation
- getVarianceDescription
  
  public static java.lang.String getVarianceDescription()
  
  Returns a descriptive label of the variance.
  
  Returns:
  
  a descriptive label of the variance
- getMedianDescription
  
  public static java.lang.String getMedianDescription()
  
  Returns a descriptive label of the median.
  
  Returns:
  
  a descriptive label of the median
- getInterquartileRangeDescription
  
  public static java.lang.String getInterquartileRangeDescription()
  
  Returns a descriptive label of the interquartile range (IQR).
  
  Returns:
  
  a descriptive label of the interquartile range (IQR)
- getPercentileDescription
  
  public static java.lang.String getPercentileDescription()
  
  Returns a descriptive label of a percentile.
  
  Returns:
  
  a descriptive label of a percentile
- getSkewnessDescription
  
  public static java.lang.String getSkewnessDescription()
  
  Returns a descriptive label of the skewness.
  
  Returns:
  
  a descriptive label of the skewness
- getKurtosisDescription
  
  public static java.lang.String getKurtosisDescription()
  
  Returns a descriptive label of the kurtosis.
  
  Returns:
  
  a descriptive label of the kurtosis
- getSkewnessInterpretation
  
  public java.lang.String getSkewnessInterpretation()
  
  Returns a qualitative description of the skewness based on its test statistic.
  
  Returns:
  
  a qualitative description of the skewness
- getKurtosisInterpretation
  
  public java.lang.String getKurtosisInterpretation()
  
  Returns a qualitative description of the kurtosis based on its test statistic.
  
  Returns:
  
  a qualitative description of the kurtosis

Class EmpiricalDistribution

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Details

EmpiricalDistribution

EmpiricalDistribution

EmpiricalDistribution

EmpiricalDistribution

Method Details

getData

getSortedData

setData

setData

clear

analyse

getCDF

getPercentile

getPercentile

getPercentiles

getXMinimum

getXMaximum

getXRange

getKDEXMinimum

getKDEXMaximum

getKDEXRange

getMedian

getInterquartileRange

recalculatePDF

recalculatePDF

calculateKDEPDFBandwidth

estimateKDEPDF

getNrOfHistogramBins

getHistogramBinCount

getHistogramBinCounts

getHistogramBinFrequency

getHistogramBinFrequencies

getHistogramBinCentre

getHistogramBinCentres

getHistogramBinWidth

getPDF

getKDEPDF

getFullKDEPDF

getN

getExpectedValue

getMean

getTrimmedMean

getKDEPDFModes

getVariance

getStandardDeviation

getSkewness

getSkewnessConfidenceBounds

getSkewnessZStatistic

getKurtosis

getKurtosisZStatistic

getJarqueBeraTestStatistic

isJarqueBeraTestAccepted

getChiSquare

getZScores

getOutliers

getMeanDescription

getStandardDeviationDescription

getVarianceDescription

getMedianDescription

getInterquartileRangeDescription

getPercentileDescription

getSkewnessDescription

getKurtosisDescription

getSkewnessInterpretation

getKurtosisInterpretation