Descriptive (WordHoard)

Overview

Package

Class

Tree

Deprecated

Index

Help

PREV CLASS NEXT CLASS

FRAMES NO FRAMES

SUMMARY: NESTED | FIELD | CONSTR | METHOD

DETAIL: FIELD | CONSTR | METHOD

edu.northwestern.at.utils.math.statistics
Class Descriptive

java.lang.Object
  edu.northwestern.at.utils.math.statistics.Descriptive

public class Descriptive
extends java.lang.Object
extends java.lang.Object

Basic descriptive statistics.

Version:: 0.91, 08-Dec-99
Author:: peter.gedeck@pharma.Novartis.com, wolfgang.hoschek@cern.ch

Constructor Summary
`protected`	`Descriptive()` Makes this class non instantiable, but still let's others inherit from it.

Method Summary
`static double`	`autoCorrelation(double[] 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(double[] data1, double standardDev1, double[] data2, double standardDev2)` Returns the correlation of two data sequences.
`static double`	`covariance(double[] data1, double[] 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)))`.
`static double`	`durbinWatson(double[] data)` Durbin-Watson computation.
`static void`	`frequencies(double[] sortedData, java.util.ArrayList distinctValues, java.util.ArrayList frequencies)` Computes the frequency (number of occurances, count) of each distinct value in the given sorted data.
`static double`	`geometricMean(double[] data)` Returns the geometric mean of a data sequence.
`static double`	`geometricMean(int size, double sumOfLogarithms)` 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(double[] 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(double[] 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(double[] data, double[] 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[] data, double mean, double standardDeviation)` Returns the kurtosis (aka excess) of a data sequence, which is `-3 + moment(data,4,mean) / standardDeviation⁴`.
`static double`	`kurtosis(double moment4, double standardDeviation)` Returns the kurtosis (aka excess) of a data sequence.
`static double`	`lag1(double[] data, double mean)` Returns the lag-1 autocorrelation of a dataset; Note that this method has semantics different from `autoCorrelation(..., 1)`;
`static double`	`max(double[] data)` Returns the largest member of a data sequence.
`static double`	`mean(double[] data)` Returns the arithmetic mean of a data sequence; That is `Sum( data[i] ) / data.length`.
`static double`	`meanDeviation(double[] data, double mean)` Returns the mean deviation of a dataset.
`static double`	`median(double[] sortedData)` Returns the median of a sorted data sequence.
`static double`	`min(double[] data)` Returns the smallest member of a data sequence.
`static double`	`moment(double[] 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.length`.
`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.length`.
`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(double[] data)` Returns the product of a data sequence, which is `Prod( data[i] )`.
`static double`	`product(int size, double sumOfLogarithms)` Returns the product, which is `Prod( data[i] )`.
`static double`	`quantile(double[] 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(double[] sortedList, double element)` Returns how many percent of the elements contained in the receiver are `<= element`.
`static double[]`	`quantiles(double[] sortedData, double[] percentages)` Returns the quantiles of the specified percentages.
`static double`	`rankInterpolated(double[] 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(double[] data, double mean, double sampleVariance)` Returns the sample kurtosis (aka excess) 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`	`sampleKurtosisStandardError(int size)` Return the standard error of the sample kurtosis.
`static double`	`sampleSkew(double[] data, double mean, double sampleVariance)` Returns the sample skew of a data sequence.
`static double`	`sampleSkew(int size, double moment3, 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(double[] data, double mean)` Returns the sample variance of a data sequence.
`static double`	`sampleVariance(int size, double sum, double sumOfSquares)` 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[] data, double mean, double standardDeviation)` Returns the skew of a data sequence, which is `moment(data,3,mean) / standardDeviation³`.
`static double`	`skew(double moment3, double standardDeviation)` Returns the skew of a data sequence.
`static java.util.ArrayList[]`	`split(double[] sortedList, double[] 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(double[] data, double mean, double standardDeviation)` Modifies a data sequence to be standardized.
`static double`	`sum(double[] data)` Returns the sum of a data sequence.
`static double`	`sumOfInversions(double[] data, int from, int to)` Returns the sum of inversions of a data sequence, which is `Sum( 1.0 / data[i])`.
`static double`	`sumOfLogarithms(double[] data, int from, int to)` Returns the sum of logarithms of a data sequence, which is `Sum( Log(data[i])`.
`static double`	`sumOfPowerDeviations(double[] data, int k, double c)` Returns sums of power deviations.
`static double`	`sumOfPowerDeviations(double[] data, int k, double c, int from, int to)` Returns sums of power deviations.
`static double`	`sumOfPowers(double[] 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(double[] data)` Returns the sum of squares of a data sequence.
`static double`	`trimmedMean(double[] 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(double[] data, double[] 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(double[] sortedData, double mean, int left, int right)` Returns the winsorized mean of a sorted data sequence.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

Descriptive

protected Descriptive()

Makes this class non instantiable, but still let's others inherit from it.

Method Detail

autoCorrelation

public static double autoCorrelation(double[] data,
                                     int lag,
                                     double mean,
                                     double variance)

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:: java.lang.IndexOutOfBoundsException - if to!=from-1 || from<0 || from>to || to>=size().

correlation

public static double correlation(double[] data1,
                                 double standardDev1,
                                 double[] data2,
                                 double standardDev2)

Returns the correlation of two data sequences. That is covariance(data1,data2)/(standardDev1*standardDev2).

covariance

public static double covariance(double[] data1,
                                double[] 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))). See the math definition.

durbinWatson

public static double durbinWatson(double[] data)

Durbin-Watson computation.

frequencies

public static void frequencies(double[] sortedData,
                               java.util.ArrayList distinctValues,
                               java.util.ArrayList 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.

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

public static double geometricMean(double[] data)

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.length). This method tries to avoid overflows at the expense of an equivalent but somewhat slow definition: geo = Math.exp( Sum( Log(data[i]) ) / data.length).

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]).

incrementalUpdate

public static void incrementalUpdate(double[] data,
                                     int from,
                                     int to,
                                     double[] inOut)

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.

If no data sequence elements have so far been recorded set the values as follows

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.

Returns the updated values filled into the inOut array.

incrementalUpdateSumsOfPowers

public static void incrementalUpdateSumsOfPowers(double[] 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.

The moment of k-th order with constant c of a data sequence, is given by Sum( (data[i]-c)^k ) / data.length. It can incrementally be computed by using the equivalent formula

moment(k,c) = m(k,c) / data.length where
m(k,c) = Sum( -1ⁱ * b(k,i) * cⁱ * sumOfPowers(k-i)) for i = 0 .. k and
b(k,i) = binomial(k,i) and
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].

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).

If no data sequence elements have so far been recorded set all old values of the sums to 0.0.

Returns the updated values filled into the sumOfPowers array.

incrementalWeightedUpdate

public static void incrementalWeightedUpdate(double[] data,
                                             double[] 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.

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.

If no data sequence elements have so far been recorded set the values as follows

inOut[0] = 0.0 as the old sum.
inOut[1] = 0.0 as the old sum of squares.

Returns the updated values filled into the inOut array.

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.

kurtosis

public static double kurtosis(double[] data,
                              double mean,
                              double standardDeviation)

Returns the kurtosis (aka excess) of a data sequence, which is -3 + moment(data,4,mean) / standardDeviation⁴.

lag1

public static double lag1(double[] data,
                          double mean)

Returns the lag-1 autocorrelation of a dataset; Note that this method has semantics different from autoCorrelation(..., 1);

max

public static double max(double[] data)

Returns the largest member of a data sequence.

mean

public static double mean(double[] data)

Returns the arithmetic mean of a data sequence; That is Sum( data[i] ) / data.length.

meanDeviation

public static double meanDeviation(double[] data,
                                   double mean)

Returns the mean deviation of a dataset. That is Sum (Math.abs(data[i]-mean)) / data.length).

median

public static double median(double[] sortedData)

Returns the median of a sorted data sequence.

Parameters:: sortedData - the data sequence; must be sorted ascending.

min

public static double min(double[] data)

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.length.

Parameters:: sumOfPowers - sumOfPowers[m] == Sum( data[i]^m) ) for m = 0,1,..,k as returned by method incrementalUpdateSumsOfPowers(double[],int,int,int,int,double[]). In particular there must hold sumOfPowers.length == k+1.; size - the number of elements of the data sequence.

moment

public static double moment(double[] 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.length.

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.

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.

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.length-1]. This method uses the equivalent definition: prod = pow( exp( Sum( Log(x[i]) ) / size(), size()).

product

public static double product(double[] data)

Returns the product of a data sequence, which is Prod( data[i] ). In other words: data[0]*data[1]*...*data[data.length-1]. Note that you may easily get numeric overflows.

quantile

public static double quantile(double[] 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. 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.

quantileInverse

public static double quantileInverse(double[] sortedList,
                                     double element)

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).

quantiles

public static double[] quantiles(double[] sortedData,
                                 double[] percentages)

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.

rankInterpolated

public static double rankInterpolated(double[] sortedList,
                                      double element)

Returns the linearly interpolated number of elements in a list less or equal to a given element. The rank is the number of elements <= element. Ranks are of the form {0, 1, 2,..., sortedList.size()}. If no element is <= 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.

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.length). 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:: sumOfSquares - sumOfSquares(data) == Sum( data[i]*data[i] ) of the data sequence.; size - the number of elements in the data sequence.

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.

sampleKurtosis

public static double sampleKurtosis(double[] data,
                                    double mean,
                                    double sampleVariance)

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.

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.

sampleSkew

public static double sampleSkew(double[] data,
                                double mean,
                                double sampleVariance)

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.

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.

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] ).

sampleVariance

public static double sampleVariance(double[] data,
                                    double mean)

Returns the sample variance of a data sequence. That is Sum ( (data[i]-mean)^2 ) / (data.length-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] ).

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.

skew

public static double skew(double[] data,
                          double mean,
                          double standardDeviation)

Returns the skew of a data sequence, which is moment(data,3,mean) / standardDeviation³.

split

public static java.util.ArrayList[] split(double[] sortedList,
                                          double[] splitters)

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:

data = (1,2,3,4,5,8,8,8,10,11)

splitters=(2,8)

(1), (2,3,4,5) (8,8,8,10,11)

splitters=()

(1,2,3,4,5,8,8,8,10,11)

splitters=(-5)

(), (1,2,3,4,5,8,8,8,10,11)

splitters=(100)

(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.

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.

standardize

public static void standardize(double[] data,
                               double mean,
                               double standardDeviation)

Modifies a data sequence to be standardized. Changes each element data[i] as follows: data[i] = (data[i]-mean)/standardDeviation.

sum

public static double sum(double[] data)

Returns the sum of a data sequence. That is Sum( data[i] ).

sumOfInversions

public static double sumOfInversions(double[] data,
                                     int from,
                                     int to)

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).

sumOfLogarithms

public static double sumOfLogarithms(double[] data,
                                     int from,
                                     int to)

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).

sumOfPowerDeviations

public static double sumOfPowerDeviations(double[] data,
                                          int k,
                                          double c)

Returns sums of power deviations.

Parameters:: data - The data as a double vector.; k - The exponent.; c - The central value.

sumOfPowerDeviations

public static double sumOfPowerDeviations(double[] data,
                                          int k,
                                          double c,
                                          int from,
                                          int to)

Returns sums of power deviations.

Parameters:: data - The data as a double vector.; k - The exponent.; c - The central value.; from - Starting data value index.; to - Ending data value index.

sumOfPowers

public static double sumOfPowers(double[] data,
                                 int k)

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.

sumOfSquares

public static double sumOfSquares(double[] data)

Returns the sum of squares of a data sequence. That is Sum ( data[i]*data[i] ).

trimmedMean

public static double trimmedMean(double[] sortedData,
                                 double mean,
                                 int left,
                                 int right)

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.; left - the number of leading elements to trim.; right - the number of trailing elements to trim.

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] ).

weightedMean

public static double weightedMean(double[] data,
                                  double[] weights)

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] ).

winsorizedMean

public static double winsorizedMean(double[] sortedData,
                                    double mean,
                                    int left,
                                    int right)

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.; left - the number of leading elements to trim.; right - the number of trailing elements to trim.

Overview

Package

Class

Tree

Deprecated

Index

Help

PREV CLASS NEXT CLASS

FRAMES NO FRAMES

SUMMARY: NESTED | FIELD | CONSTR | METHOD

DETAIL: FIELD | CONSTR | METHOD

edu.northwestern.at.utils.math.statistics Class Descriptive

Descriptive

autoCorrelation

checkRangeFromTo

correlation

covariance

durbinWatson

frequencies

geometricMean

geometricMean

harmonicMean

incrementalUpdate

incrementalUpdateSumsOfPowers

incrementalWeightedUpdate

kurtosis

kurtosis

lag1

max

mean

meanDeviation

median

min

moment

moment

pooledMean

pooledVariance

product

product

quantile

quantileInverse

quantiles

rankInterpolated

rms

sampleKurtosis

sampleKurtosis

sampleKurtosisStandardError

sampleSkew

sampleSkew

sampleSkewStandardError

sampleStandardDeviation

sampleVariance

sampleVariance

sampleWeightedVariance

skew

skew

split

standardDeviation

standardError

standardize

sum

sumOfInversions

sumOfLogarithms

sumOfPowerDeviations

sumOfPowerDeviations

sumOfPowers

sumOfSquaredDeviations

sumOfSquares

trimmedMean

variance

variance

weightedMean

weightedRMS

winsorizedMean

edu.northwestern.at.utils.math.statistics
Class Descriptive