Class Descriptive
- Version:
- 0.91, 08-Dec-99
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Constructor Summary
ConstructorsModifierConstructorDescriptionprotected
Makes this class non instantiable, but still let's others inherit from it. -
Method Summary
Modifier and TypeMethodDescriptionstatic double
autoCorrelation
(DoubleArrayList data, int lag, double mean, double variance) Returns the auto-correlation of a data sequence.protected static void
checkRangeFromTo
(int from, int to, int theSize) Checks if the given range is within the contained array's bounds.static double
correlation
(DoubleArrayList data1, double standardDev1, DoubleArrayList data2, double standardDev2) Returns the correlation of two data sequences.static double
covariance
(DoubleArrayList data1, DoubleArrayList data2) Returns the covariance of two data sequences, which is cov(x,y) = (1/(size()-1)) * Sum((x[i]-mean(x)) * (y[i]-mean(y))).private static double
covariance2
(DoubleArrayList data1, DoubleArrayList data2) static double
durbinWatson
(DoubleArrayList data) Durbin-Watson computation.static void
frequencies
(DoubleArrayList sortedData, DoubleArrayList distinctValues, IntArrayList frequencies) Computes the frequency (number of occurances, count) of each distinct value in the given sorted data.static double
geometricMean
(int size, double sumOfLogarithms) Returns the geometric mean of a data sequence.static double
geometricMean
(DoubleArrayList data) Returns the geometric mean of a data sequence.static double
harmonicMean
(int size, double sumOfInversions) Returns the harmonic mean of a data sequence.static void
incrementalUpdate
(DoubleArrayList data, int from, int to, double[] inOut) Incrementally maintains and updates minimum, maximum, sum and sum of squares of a data sequence.static void
incrementalUpdateSumsOfPowers
(DoubleArrayList data, int from, int to, int fromSumIndex, int toSumIndex, double[] sumOfPowers) Incrementally maintains and updates various sums of powers of the form Sum(data[i]k).static void
incrementalWeightedUpdate
(DoubleArrayList data, DoubleArrayList weights, int from, int to, double[] inOut) Incrementally maintains and updates sum and sum of squares of a weighted data sequence.static double
kurtosis
(double moment4, double standardDeviation) Returns the kurtosis (aka excess) of a data sequence.static double
kurtosis
(DoubleArrayList data, double mean, double standardDeviation) Returns the kurtosis (aka excess) of a data sequence, which is -3 + moment(data,4,mean) / standardDeviation4.static double
lag1
(DoubleArrayList data, double mean) Returns the lag-1 autocorrelation of a dataset; Note that this method has semantics different from autoCorrelation(..., 1);static double
max
(DoubleArrayList data) Returns the largest member of a data sequence.static double
mean
(DoubleArrayList data) Returns the arithmetic mean of a data sequence; That is Sum( data[i] ) / data.size().static double
meanDeviation
(DoubleArrayList data, double mean) Returns the mean deviation of a dataset.static double
median
(DoubleArrayList sortedData) Returns the median of a sorted data sequence.static double
min
(DoubleArrayList data) Returns the smallest member of a data sequence.static double
moment
(int k, double c, int size, double[] sumOfPowers) Returns the moment of k-th order with constant c of a data sequence, which is Sum( (data[i]-c)k ) / data.size().static double
moment
(DoubleArrayList data, int k, double c) Returns the moment of k-th order with constant c of a data sequence, which is Sum( (data[i]-c)k ) / data.size().static double
pooledMean
(int size1, double mean1, int size2, double mean2) Returns the pooled mean of two data sequences.static double
pooledVariance
(int size1, double variance1, int size2, double variance2) Returns the pooled variance of two data sequences.static double
product
(int size, double sumOfLogarithms) Returns the product, which is Prod( data[i] ).static double
product
(DoubleArrayList data) Returns the product of a data sequence, which is Prod( data[i] ).static double
quantile
(DoubleArrayList sortedData, double phi) Returns the phi-quantile; that is, an element elem for which holds that phi percent of data elements are less than elem.static double
quantileInverse
(DoubleArrayList sortedList, double element) Returns how many percent of the elements contained in the receiver are <= element.static DoubleArrayList
quantiles
(DoubleArrayList sortedData, DoubleArrayList percentages) Returns the quantiles of the specified percentages.static double
rankInterpolated
(DoubleArrayList sortedList, double element) Returns the linearly interpolated number of elements in a list less or equal to a given element.static double
rms
(int size, double sumOfSquares) Returns the RMS (Root-Mean-Square) of a data sequence.static double
sampleKurtosis
(int size, double moment4, double sampleVariance) Returns the sample kurtosis (aka excess) of a data sequence.static double
sampleKurtosis
(DoubleArrayList data, double mean, double sampleVariance) Returns the sample kurtosis (aka excess) of a data sequence.static double
sampleKurtosisStandardError
(int size) Return the standard error of the sample kurtosis.static double
sampleSkew
(int size, double moment3, double sampleVariance) Returns the sample skew of a data sequence.static double
sampleSkew
(DoubleArrayList data, double mean, double sampleVariance) Returns the sample skew of a data sequence.static double
sampleSkewStandardError
(int size) Return the standard error of the sample skew.static double
sampleStandardDeviation
(int size, double sampleVariance) Returns the sample standard deviation.static double
sampleVariance
(int size, double sum, double sumOfSquares) Returns the sample variance of a data sequence.static double
sampleVariance
(DoubleArrayList data, double mean) Returns the sample variance of a data sequence.static double
sampleWeightedVariance
(double sumOfWeights, double sumOfProducts, double sumOfSquaredProducts) Returns the sample weighted variance of a data sequence.static double
skew
(double moment3, double standardDeviation) Returns the skew of a data sequence.static double
skew
(DoubleArrayList data, double mean, double standardDeviation) Returns the skew of a data sequence, which is moment(data,3,mean) / standardDeviation3.static DoubleArrayList[]
split
(DoubleArrayList sortedList, DoubleArrayList splitters) Splits (partitions) a list into sublists such that each sublist contains the elements with a given range.static double
standardDeviation
(double variance) Returns the standard deviation from a variance.static double
standardError
(int size, double variance) Returns the standard error of a data sequence.static void
standardize
(DoubleArrayList data, double mean, double standardDeviation) Modifies a data sequence to be standardized.static double
sum
(DoubleArrayList data) Returns the sum of a data sequence.static double
sumOfInversions
(DoubleArrayList data, int from, int to) Returns the sum of inversions of a data sequence, which is Sum( 1.0 / data[i]).static double
sumOfLogarithms
(DoubleArrayList data, int from, int to) Returns the sum of logarithms of a data sequence, which is Sum( Log(data[i]).static double
sumOfPowerDeviations
(DoubleArrayList data, int k, double c) Returns Sum( (data[i]-c)k ); optimized for common parameters like c == 0.0 and/or k == -2 ..static double
sumOfPowerDeviations
(DoubleArrayList data, int k, double c, int from, int to) Returns Sum( (data[i]-c)k ) for all i = from ..static double
sumOfPowers
(DoubleArrayList data, int k) Returns the sum of powers of a data sequence, which is Sum ( data[i]k ).static double
sumOfSquaredDeviations
(int size, double variance) Returns the sum of squared mean deviation of of a data sequence.static double
sumOfSquares
(DoubleArrayList data) Returns the sum of squares of a data sequence.static double
trimmedMean
(DoubleArrayList sortedData, double mean, int left, int right) Returns the trimmed mean of a sorted data sequence.static double
variance
(double standardDeviation) Returns the variance from a standard deviation.static double
variance
(int size, double sum, double sumOfSquares) Returns the variance of a data sequence.static double
weightedMean
(DoubleArrayList data, DoubleArrayList weights) Returns the weighted mean of a data sequence.static double
weightedRMS
(double sumOfProducts, double sumOfSquaredProducts) Returns the weighted RMS (Root-Mean-Square) of a data sequence.static double
winsorizedMean
(DoubleArrayList sortedData, double mean, int left, int right) Returns the winsorized mean of a sorted data sequence.
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Constructor Details
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Descriptive
protected Descriptive()Makes this class non instantiable, but still let's others inherit from it.
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Method Details
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autoCorrelation
Returns the auto-correlation of a data sequence. -
checkRangeFromTo
protected static void checkRangeFromTo(int from, int to, int theSize) Checks if the given range is within the contained array's bounds.- Throws:
IndexOutOfBoundsException
- if to!=from-1 || from<0 || from>to || to>=size().
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correlation
public static double correlation(DoubleArrayList data1, double standardDev1, DoubleArrayList data2, double standardDev2) Returns the correlation of two data sequences. That is covariance(data1,data2)/(standardDev1*standardDev2). -
covariance
Returns the covariance of two data sequences, which is cov(x,y) = (1/(size()-1)) * Sum((x[i]-mean(x)) * (y[i]-mean(y))). See the math definition. -
covariance2
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durbinWatson
Durbin-Watson computation. -
frequencies
public static void frequencies(DoubleArrayList sortedData, DoubleArrayList distinctValues, IntArrayList frequencies) Computes the frequency (number of occurances, count) of each distinct value in the given sorted data. After this call returns both distinctValues and frequencies have a new size (which is equal for both), which is the number of distinct values in the sorted data.Distinct values are filled into distinctValues, starting at index 0. The frequency of each distinct value is filled into frequencies, starting at index 0. As a result, the smallest distinct value (and its frequency) can be found at index 0, the second smallest distinct value (and its frequency) at index 1, ..., the largest distinct value (and its frequency) at index distinctValues.size()-1. Example:
elements = (5,6,6,7,8,8) --> distinctValues = (5,6,7,8), frequencies = (1,2,1,2)- Parameters:
sortedData
- the data; must be sorted ascending.distinctValues
- a list to be filled with the distinct values; can have any size.frequencies
- a list to be filled with the frequencies; can have any size; set this parameter to null to ignore it.
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geometricMean
public static double geometricMean(int size, double sumOfLogarithms) Returns the geometric mean of a data sequence. Note that for a geometric mean to be meaningful, the minimum of the data sequence must not be less or equal to zero.
The geometric mean is given by pow( Product( data[i] ), 1/size) which is equivalent to Math.exp( Sum( Log(data[i]) ) / size). -
geometricMean
Returns the geometric mean of a data sequence. Note that for a geometric mean to be meaningful, the minimum of the data sequence must not be less or equal to zero.
The geometric mean is given by pow( Product( data[i] ), 1/data.size()). This method tries to avoid overflows at the expense of an equivalent but somewhat slow definition: geo = Math.exp( Sum( Log(data[i]) ) / data.size()). -
harmonicMean
public static double harmonicMean(int size, double sumOfInversions) Returns the harmonic mean of a data sequence.- Parameters:
size
- the number of elements in the data sequence.sumOfInversions
- Sum( 1.0 / data[i]).
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incrementalUpdate
Incrementally maintains and updates minimum, maximum, sum and sum of squares of a data sequence. Assume we have already recorded some data sequence elements and know their minimum, maximum, sum and sum of squares. Assume further, we are to record some more elements and to derive updated values of minimum, maximum, sum and sum of squares.This method computes those updated values without needing to know the already recorded elements. This is interesting for interactive online monitoring and/or applications that cannot keep the entire huge data sequence in memory.
Definition of sumOfSquares: sumOfSquares(n) = Sum ( data[i] * data[i] ).- Parameters:
data
- the additional elements to be incorporated into min, max, etc.from
- the index of the first element within data to consider.to
- the index of the last element within data to consider. The method incorporates elements data[from], ..., data[to].inOut
- the old values in the following format:- inOut[0] is the old minimum.
- inOut[1] is the old maximum.
- inOut[2] is the old sum.
- inOut[3] is the old sum of squares.
- inOut[0] = Double.POSITIVE_INFINITY as the old minimum.
- inOut[1] = Double.NEGATIVE_INFINITY as the old maximum.
- inOut[2] = 0.0 as the old sum.
- inOut[3] = 0.0 as the old sum of squares.
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incrementalUpdateSumsOfPowers
public static void incrementalUpdateSumsOfPowers(DoubleArrayList data, int from, int to, int fromSumIndex, int toSumIndex, double[] sumOfPowers) Incrementally maintains and updates various sums of powers of the form Sum(data[i]k). Assume we have already recorded some data sequence elements data[i] and know the values of Sum(data[i]from), Sum(data[i]from+1), ..., Sum(data[i]to). Assume further, we are to record some more elements and to derive updated values of these sums.This method computes those updated values without needing to know the already recorded elements. This is interesting for interactive online monitoring and/or applications that cannot keep the entire huge data sequence in memory. For example, the incremental computation of moments is based upon such sums of powers:
The moment of k-th order with constant c of a data sequence, is given by Sum( (data[i]-c)k ) / data.size(). It can incrementally be computed by using the equivalent formula
moment(k,c) = m(k,c) / data.size() where
m(k,c) = Sum( -1i * b(k,i) * ci * sumOfPowers(k-i)) for i = 0 .. k and
b(k,i) =binomial(k,i)
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sumOfPowers(k) = Sum( data[i]k ).- Parameters:
data
- the additional elements to be incorporated into min, max, etc.from
- the index of the first element within data to consider.to
- the index of the last element within data to consider. The method incorporates elements data[from], ..., data[to].inOut
- the old values of the sums in the following format:- sumOfPowers[0] is the old Sum(data[i]fromSumIndex).
- sumOfPowers[1] is the old Sum(data[i]fromSumIndex+1).
- ...
- sumOfPowers[toSumIndex-fromSumIndex] is the old Sum(data[i]toSumIndex).
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incrementalWeightedUpdate
public static void incrementalWeightedUpdate(DoubleArrayList data, DoubleArrayList weights, int from, int to, double[] inOut) Incrementally maintains and updates sum and sum of squares of a weighted data sequence. Assume we have already recorded some data sequence elements and know their sum and sum of squares. Assume further, we are to record some more elements and to derive updated values of sum and sum of squares.This method computes those updated values without needing to know the already recorded elements. This is interesting for interactive online monitoring and/or applications that cannot keep the entire huge data sequence in memory.
Definition of sum: sum = Sum ( data[i] * weights[i] ).
Definition of sumOfSquares: sumOfSquares = Sum ( data[i] * data[i] * weights[i]).- Parameters:
data
- the additional elements to be incorporated into min, max, etc.weights
- the weight of each element within data.from
- the index of the first element within data (and weights) to consider.to
- the index of the last element within data (and weights) to consider. The method incorporates elements data[from], ..., data[to].inOut
- the old values in the following format:- inOut[0] is the old sum.
- inOut[1] is the old sum of squares.
- inOut[0] = 0.0 as the old sum.
- inOut[1] = 0.0 as the old sum of squares.
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kurtosis
public static double kurtosis(double moment4, double standardDeviation) Returns the kurtosis (aka excess) of a data sequence.- Parameters:
moment4
- the fourth central moment, which is moment(data,4,mean).standardDeviation
- the standardDeviation.
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kurtosis
Returns the kurtosis (aka excess) of a data sequence, which is -3 + moment(data,4,mean) / standardDeviation4. -
lag1
Returns the lag-1 autocorrelation of a dataset; Note that this method has semantics different from autoCorrelation(..., 1); -
max
Returns the largest member of a data sequence. -
mean
Returns the arithmetic mean of a data sequence; That is Sum( data[i] ) / data.size(). -
meanDeviation
Returns the mean deviation of a dataset. That is Sum (Math.abs(data[i]-mean)) / data.size()). -
median
Returns the median of a sorted data sequence.- Parameters:
sortedData
- the data sequence; must be sorted ascending.
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min
Returns the smallest member of a data sequence. -
moment
public static double moment(int k, double c, int size, double[] sumOfPowers) Returns the moment of k-th order with constant c of a data sequence, which is Sum( (data[i]-c)k ) / data.size().- Parameters:
size
- the number of elements of the data sequence.sumOfPowers
- sumOfPowers[m] == Sum( data[i]m) ) for m = 0,1,..,k as returned by methodincrementalUpdateSumsOfPowers(DoubleArrayList,int,int,int,int,double[])
. In particular there must hold sumOfPowers.length == k+1.
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moment
Returns the moment of k-th order with constant c of a data sequence, which is Sum( (data[i]-c)k ) / data.size(). -
pooledMean
public static double pooledMean(int size1, double mean1, int size2, double mean2) Returns the pooled mean of two data sequences. That is (size1 * mean1 + size2 * mean2) / (size1 + size2).- Parameters:
size1
- the number of elements in data sequence 1.mean1
- the mean of data sequence 1.size2
- the number of elements in data sequence 2.mean2
- the mean of data sequence 2.
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pooledVariance
public static double pooledVariance(int size1, double variance1, int size2, double variance2) Returns the pooled variance of two data sequences. That is (size1 * variance1 + size2 * variance2) / (size1 + size2);- Parameters:
size1
- the number of elements in data sequence 1.variance1
- the variance of data sequence 1.size2
- the number of elements in data sequence 2.variance2
- the variance of data sequence 2.
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product
public static double product(int size, double sumOfLogarithms) Returns the product, which is Prod( data[i] ). In other words: data[0]*data[1]*...*data[data.size()-1]. This method uses the equivalent definition: prod = pow( exp( Sum( Log(x[i]) ) / size(), size()). -
product
Returns the product of a data sequence, which is Prod( data[i] ). In other words: data[0]*data[1]*...*data[data.size()-1]. Note that you may easily get numeric overflows. -
quantile
Returns the phi-quantile; that is, an element elem for which holds that phi percent of data elements are less than elem. The quantile need not necessarily be contained in the data sequence, it can be a linear interpolation.- Parameters:
sortedData
- the data sequence; must be sorted ascending.phi
- the percentage; must satisfy 0 <= phi <= 1.
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quantileInverse
Returns how many percent of the elements contained in the receiver are <= element. Does linear interpolation if the element is not contained but lies in between two contained elements.- Parameters:
sortedList
- the list to be searched (must be sorted ascending).element
- the element to search for.- Returns:
- the percentage phi of elements <= element (0.0 <= phi <= 1.0).
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quantiles
Returns the quantiles of the specified percentages. The quantiles need not necessarily be contained in the data sequence, it can be a linear interpolation.- Parameters:
sortedData
- the data sequence; must be sorted ascending.percentages
- the percentages for which quantiles are to be computed. Each percentage must be in the interval [0.0,1.0].- Returns:
- the quantiles.
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rankInterpolated
Returns the linearly interpolated number of elements in a list less or equal to a given element. The rank is the number of elements invalid input: '<'= element. Ranks are of the form {0, 1, 2,..., sortedList.size()}. If no element is invalid input: '<'= element, then the rank is zero. If the element lies in between two contained elements, then linear interpolation is used and a non integer value is returned.- Parameters:
sortedList
- the list to be searched (must be sorted ascending).element
- the element to search for.- Returns:
- the rank of the element.
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rms
public static double rms(int size, double sumOfSquares) Returns the RMS (Root-Mean-Square) of a data sequence. That is Math.sqrt(Sum( data[i]*data[i] ) / data.size()). The RMS of data sequence is the square-root of the mean of the squares of the elements in the data sequence. It is a measure of the average "size" of the elements of a data sequence.- Parameters:
size
- the number of elements in the data sequence.sumOfSquares
- sumOfSquares(data) == Sum( data[i]*data[i] ) of the data sequence.
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sampleKurtosis
public static double sampleKurtosis(int size, double moment4, double sampleVariance) Returns the sample kurtosis (aka excess) of a data sequence. Ref: R.R. Sokal, F.J. Rohlf, Biometry: the principles and practice of statistics in biological research (W.H. Freeman and Company, New York, 1998, 3rd edition) p. 114-115.- Parameters:
size
- the number of elements of the data sequence.moment4
- the fourth central moment, which is moment(data,4,mean).sampleVariance
- the sample variance.
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sampleKurtosis
Returns the sample kurtosis (aka excess) of a data sequence. -
sampleKurtosisStandardError
public static double sampleKurtosisStandardError(int size) Return the standard error of the sample kurtosis. Ref: R.R. Sokal, F.J. Rohlf, Biometry: the principles and practice of statistics in biological research (W.H. Freeman and Company, New York, 1998, 3rd edition) p. 138.- Parameters:
size
- the number of elements of the data sequence.
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sampleSkew
public static double sampleSkew(int size, double moment3, double sampleVariance) Returns the sample skew of a data sequence. Ref: R.R. Sokal, F.J. Rohlf, Biometry: the principles and practice of statistics in biological research (W.H. Freeman and Company, New York, 1998, 3rd edition) p. 114-115.- Parameters:
size
- the number of elements of the data sequence.moment3
- the third central moment, which is moment(data,3,mean).sampleVariance
- the sample variance.
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sampleSkew
Returns the sample skew of a data sequence. -
sampleSkewStandardError
public static double sampleSkewStandardError(int size) Return the standard error of the sample skew. Ref: R.R. Sokal, F.J. Rohlf, Biometry: the principles and practice of statistics in biological research (W.H. Freeman and Company, New York, 1998, 3rd edition) p. 138.- Parameters:
size
- the number of elements of the data sequence.
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sampleStandardDeviation
public static double sampleStandardDeviation(int size, double sampleVariance) Returns the sample standard deviation. Ref: R.R. Sokal, F.J. Rohlf, Biometry: the principles and practice of statistics in biological research (W.H. Freeman and Company, New York, 1998, 3rd edition) p. 53.- Parameters:
size
- the number of elements of the data sequence.sampleVariance
- the sample variance.
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sampleVariance
public static double sampleVariance(int size, double sum, double sumOfSquares) Returns the sample variance of a data sequence. That is (sumOfSquares - mean*sum) / (size - 1) with mean = sum/size.- Parameters:
size
- the number of elements of the data sequence.sum
- == Sum( data[i] ).sumOfSquares
- == Sum( data[i]*data[i] ).
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sampleVariance
Returns the sample variance of a data sequence. That is Sum ( (data[i]-mean)^2 ) / (data.size()-1). -
sampleWeightedVariance
public static double sampleWeightedVariance(double sumOfWeights, double sumOfProducts, double sumOfSquaredProducts) Returns the sample weighted variance of a data sequence. That is (sumOfSquaredProducts - sumOfProducts * sumOfProducts / sumOfWeights) / (sumOfWeights - 1).- Parameters:
sumOfWeights
- == Sum( weights[i] ).sumOfProducts
- == Sum( data[i] * weights[i] ).sumOfSquaredProducts
- == Sum( data[i] * data[i] * weights[i] ).
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skew
public static double skew(double moment3, double standardDeviation) Returns the skew of a data sequence.- Parameters:
moment3
- the third central moment, which is moment(data,3,mean).standardDeviation
- the standardDeviation.
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skew
Returns the skew of a data sequence, which is moment(data,3,mean) / standardDeviation3. -
split
Splits (partitions) a list into sublists such that each sublist contains the elements with a given range. splitters=(a,b,c,...,y,z) defines the ranges [-inf,a), [a,b), [b,c), ..., [y,z), [z,inf].Examples:
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data = (1,2,3,4,5,8,8,8,10,11).
splitters=(2,8) yields 3 bins: (1), (2,3,4,5) (8,8,8,10,11).
splitters=() yields 1 bin: (1,2,3,4,5,8,8,8,10,11).
splitters=(-5) yields 2 bins: (), (1,2,3,4,5,8,8,8,10,11).
splitters=(100) yields 2 bins: (1,2,3,4,5,8,8,8,10,11), ().- Parameters:
sortedList
- the list to be partitioned (must be sorted ascending).splitters
- the points at which the list shall be partitioned (must be sorted ascending).- Returns:
- the sublists (an array with length == splitters.size() + 1. Each sublist is returned sorted ascending.
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standardDeviation
public static double standardDeviation(double variance) Returns the standard deviation from a variance. -
standardError
public static double standardError(int size, double variance) Returns the standard error of a data sequence. That is Math.sqrt(variance/size).- Parameters:
size
- the number of elements in the data sequence.variance
- the variance of the data sequence.
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standardize
Modifies a data sequence to be standardized. Changes each element data[i] as follows: data[i] = (data[i]-mean)/standardDeviation. -
sum
Returns the sum of a data sequence. That is Sum( data[i] ). -
sumOfInversions
Returns the sum of inversions of a data sequence, which is Sum( 1.0 / data[i]).- Parameters:
data
- the data sequence.from
- the index of the first data element (inclusive).to
- the index of the last data element (inclusive).
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sumOfLogarithms
Returns the sum of logarithms of a data sequence, which is Sum( Log(data[i]).- Parameters:
data
- the data sequence.from
- the index of the first data element (inclusive).to
- the index of the last data element (inclusive).
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sumOfPowerDeviations
Returns Sum( (data[i]-c)k ); optimized for common parameters like c == 0.0 and/or k == -2 .. 4. -
sumOfPowerDeviations
Returns Sum( (data[i]-c)k ) for all i = from .. to; optimized for common parameters like c == 0.0 and/or k == -2 .. 5. -
sumOfPowers
Returns the sum of powers of a data sequence, which is Sum ( data[i]k ). -
sumOfSquaredDeviations
public static double sumOfSquaredDeviations(int size, double variance) Returns the sum of squared mean deviation of of a data sequence. That is variance * (size-1) == Sum( (data[i] - mean)^2 ).- Parameters:
size
- the number of elements of the data sequence.variance
- the variance of the data sequence.
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sumOfSquares
Returns the sum of squares of a data sequence. That is Sum ( data[i]*data[i] ). -
trimmedMean
Returns the trimmed mean of a sorted data sequence.- Parameters:
sortedData
- the data sequence; must be sorted ascending.mean
- the mean of the (full) sorted data sequence.
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variance
public static double variance(double standardDeviation) Returns the variance from a standard deviation. -
variance
public static double variance(int size, double sum, double sumOfSquares) Returns the variance of a data sequence. That is (sumOfSquares - mean*sum) / size with mean = sum/size.- Parameters:
size
- the number of elements of the data sequence.sum
- == Sum( data[i] ).sumOfSquares
- == Sum( data[i]*data[i] ).
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weightedMean
Returns the weighted mean of a data sequence. That is Sum (data[i] * weights[i]) / Sum ( weights[i] ). -
weightedRMS
public static double weightedRMS(double sumOfProducts, double sumOfSquaredProducts) Returns the weighted RMS (Root-Mean-Square) of a data sequence. That is Sum( data[i] * data[i] * weights[i]) / Sum( data[i] * weights[i] ), or in other words sumOfProducts / sumOfSquaredProducts.- Parameters:
sumOfProducts
- == Sum( data[i] * weights[i] ).sumOfSquaredProducts
- == Sum( data[i] * data[i] * weights[i] ).
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winsorizedMean
Returns the winsorized mean of a sorted data sequence.- Parameters:
sortedData
- the data sequence; must be sorted ascending.mean
- the mean of the (full) sorted data sequence.
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