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java.lang.Object peakml.math.Statistical
public abstract class Statistical
The class Statistical
contains methods for performing basis statistical operations,
such as mean, median, standard deviation. Also supported are correlation analysis, factorial
calculations, ranking, analysis of variance, etc. Basically it provides the toolbox for
performing an analysis of a set of data.
A large number of the implementation have been taken from Numerical Recipes in C.
Field Summary  

static int 
COLUMN
Indicates that the column should be processed 
static int 
MAXIMUM
The maximum value in the result of the stats(double[]) method. 
static int 
MEAN
The mean value in the result of the stats(double[]) method. 
static int 
MINIMUM
The minimum value in the result of the stats(double[]) method. 
static int 
NRSTATS
The total number of statistics in the result of the stats(double[]) method. 
static int 
PEARSON_CORRELATION
The correlation value in the result of the pearsonsCorrelation(double[], double[]) method. 
static int 
PEARSON_FISHER
The fisher transformed correlation (normally distributed) in the result of the pearsonsCorrelation(double[], double[]) method. 
static int 
PEARSON_FISHER_STDDEV
The fisher transformed standard error value in the result of the pearsonsCorrelation(double[], double[]) method. 
static int 
PEARSON_TTEST
The student's ttest value in the result of the pearsonsCorrelation(double[], double[]) method. 
static int 
QUARTILE_LOWER
The lower quartile in the result of the quartiles(double[]) method. 
static int 
QUARTILE_MEDIAN
The median quartile in the result of the quartiles(double[]) method. 
static int 
QUARTILE_UPPER
The upper quartile in the result of the quartiles(double[]) method. 
static int 
ROW
Indicates that the row should be processed 
static int 
SHAPIRO_WILK_PVALUE
The pvalue in the result of the shapiroWilk(double[]) method. 
static int 
SHAPIRO_WILK_WSTAT
The wstatistic in the result of the shapiroWilk(double[]) method. 
static int 
SPEARMAN_CORRELATION
The correlation value in the result of the spearmanCorrelation(double[], double[]) method. 
static int 
SPEARMAN_TWOSIDED_SIGNIFICANCE
The significant level in the result of the spearmanCorrelation(double[], double[]) method. 
static int 
STDDEV
The standard deviation value in the result of the stats(double[]) method. 
static int 
VARIANCE
The variance value in the result of the stats(double[]) method. 
Constructor Summary  

Statistical()

Method Summary  

static double 
beta(double z,
double w)

static double 
betacf(double a,
double b,
double x)

static double 
betai(double a,
double b,
double x)

static double 
binomialln(int n,
int k)
A binomial is a polynomial with two terms—the sum of two monomials—often bound by parenthesis or brackets when operated upon. 
static double 
durbinWatson(double[] values)
Simplistic implementation of the DurbinWatson statistic. 
static double 
durbinWatsonCERN(double[] values)
This implementation has been taken from http://www.lbl.gov/ 
static double 
factorialln(int n)
In mathematics, the factorial of a nonnegative integer n, denoted by n!, is the product of all positive integers less than or equal to n. 
static double 
ftest(double[] a,
double[] b)
An Ftest is any statistical test in which the test statistic has an Fdistribution if the null hypothesis is true. 
static double 
gammaln(double z)
The gamma function interpolates the factorial function. 
static double 
geomean(double[] values)
The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers. 
static int 
indexOfMax(double[] values)

static double 
interquartileRange(double[] values)
In descriptive statistics, the interquartile range (IQR), also called the midspread, middle fifty and middle of the #s, is a measure of statistical dispersion, being equal to the difference between the third and first quartiles. 
static double 
kthElement(double[] values,
int k)
Returns the kth smallest value in the given array. 
static double 
max(double[] values)
Calculates the maximum value from the values in the given array. 
static double 
mean(double[] values)
Calculates the mean of the values in the given array. 
static double 
median(double[] values)
Calculates the median of the values in the given array. 
static double 
min(double[] values)
Calculates the minimum value from the values in the given array. 
static void 
normalize(double[] values)
Normalizes the values in the given vector to the maximum (ie the maximum value will be 1). 
static void 
normalize(double[] values,
double max)
Normalizes the values in the given vector to given the maximum. 
static double[] 
pearsonsCorrelation(double[] xvalues,
double[] yvalues)
In statistics, the Pearson productmoment correlation coefficient (sometimes referred to as the MCV or PMCC, and typically denoted by r) is a common measure of the correlation (linear dependence) between two variables X and Y. 
static double 
pearsonsCorrelationS(double[] xvalues,
double[] yvalues)

static double[] 
permute(double[] vector)
Randomly permutes the values in the given vector. 
static double[][] 
permute(double[][] data,
int rowcolumn)
Randomly permutes the values in the given matrix. 
static void 
qsort(double[] values,
double[]... arrays)

static double[] 
quartiles(double[] values)
Quartiles partition the corresponding distribution into four quarters each containing 25% of the data. 
static double[][] 
rank(double[][] data,
boolean reversed,
int rowcolumn)
Highly optimized function for ranking the contents of a matrix either on the COLUMN or the ROW. 
static double[] 
rank(double[] data,
boolean reversed)
Highly optimized function for ranking the contents of a vector. 
static double 
rsd(double[] values)

static double[][] 
scale(double[][] data,
int rowcolumn)
Calculates the standard score for either each row or each column. 
static double[] 
shapiroWilk(double[] values)
The ShapiroWilk test tests the null hypothesis that a sample x1, ..., xn came from a normally distributed population. 
static double[] 
spearmanCorrelation(double[] xvalues,
double[] yvalues)
Calculates the Spearman rank correlation and the twosided significance levels of its deviation from zero between the two given arrays. 
static double 
spearmanCorrelationS(double[] xvalues,
double[] yvalues)

static double[] 
stats(double[] values)
Calculates some basic statistics on the given array of data. 
static double 
stddev(double[] values)
The standard deviation of a sample is one measure of statistical dispersion, calculated by taking the square root of the deviation. 
static double 
sum(double[] values)
Calculates the sum of the values in the given array. 
static double 
ttest(double[] a,
double[] b)
A ttest is any statistical hypothesis test in which the test statistic has a Student's t distribution if the null hypothesis is true. 
static double 
variance(double[] values)
The variance of a sample is one measure of statistical dispersion, averaging the squared distance of its possible values from the expected value (mean). 
Methods inherited from class java.lang.Object 

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Field Detail 

public static final int ROW
public static final int COLUMN
public static final int MINIMUM
stats(double[])
method.
public static final int MAXIMUM
stats(double[])
method.
public static final int MEAN
stats(double[])
method.
public static final int VARIANCE
stats(double[])
method.
public static final int STDDEV
stats(double[])
method.
public static final int NRSTATS
stats(double[])
method.
public static final int QUARTILE_LOWER
quartiles(double[])
method.
public static final int QUARTILE_MEDIAN
quartiles(double[])
method.
public static final int QUARTILE_UPPER
quartiles(double[])
method.
public static final int SHAPIRO_WILK_WSTAT
shapiroWilk(double[])
method.
public static final int SHAPIRO_WILK_PVALUE
shapiroWilk(double[])
method.
public static final int PEARSON_CORRELATION
pearsonsCorrelation(double[], double[])
method.
public static final int PEARSON_FISHER
pearsonsCorrelation(double[], double[])
method.
public static final int PEARSON_FISHER_STDDEV
pearsonsCorrelation(double[], double[])
method.
public static final int PEARSON_TTEST
pearsonsCorrelation(double[], double[])
method.
public static final int SPEARMAN_CORRELATION
spearmanCorrelation(double[], double[])
method.
public static final int SPEARMAN_TWOSIDED_SIGNIFICANCE
spearmanCorrelation(double[], double[])
method.
Constructor Detail 

public Statistical()
Method Detail 

public static double min(double[] values)
values
 The array with the values.
public static double max(double[] values)
values
 The array with the values.
public static int indexOfMax(double[] values)
public static double sum(double[] values)
values
 The array with the values.
public static double mean(double[] values)
values
 The array with the values.
public static double geomean(double[] values) throws java.lang.IllegalArgumentException
The geometric mean only applies to positive numbers.
values
 The array with the values.
java.lang.IllegalArgumentException
 Thrown when the array has 0 elements or the array contains one or more negative values.http://en.wikipedia.org/wiki/Geometric_mean
public static double median(double[] values)
For some fixed sizes (3,5,6,7,9) the most optimal sorting is implemented
(taken from XILINX XCELL magazine, vol. 23 by John L. Smith). The method
kthElement(double[], int)
is used for other cases.
values
 The array with the values.
public static double variance(double[] values)
values
 The array with the values.
http://en.wikipedia.org/wiki/Variance
public static double stddev(double[] values)
values
 The array with the values.
http://en.wikipedia.org/wiki/Standard_deviation
public static double rsd(double[] values)
values

public static double kthElement(double[] values, int k)
This method is taken from numerical recipes in paragraph 8.5 (select).
values
 The array with the values.k
 The index.
public static double[] stats(double[] values)
MINIMUM
, MAXIMUM
,
MEAN
, VARIANCE
and
STDDEV
.
values
 The array with the values.
public static double[] quartiles(double[] values)
values
 Array with the distribution to quartile.
http://en.wikipedia.org/wiki/Quartile
,
http://www.vias.org/tmdatanaleng/cc_quartile.html
public static double interquartileRange(double[] values)
values
 The array with the values.
http://en.wikipedia.org/wiki/Interquartile_range
public static void normalize(double[] values)
values
 The array with the values.public static void normalize(double[] values, double max)
values
 The array with the values.max
 The maximum to scale to.public static double[][] scale(double[][] data, int rowcolumn)
data
 The data matrix to be scaledrowcolumn
 Either ROW
or COLUMN
.public static double[] pearsonsCorrelation(double[] xvalues, double[] yvalues)
This implementation has been based on Numerical Recipes in C paragraph 14.5.
xvalues
 The array with the xvalues.yvalues
 The array with the yvalues.
public static double pearsonsCorrelationS(double[] xvalues, double[] yvalues)
public static double[] spearmanCorrelation(double[] xvalues, double[] yvalues)
This implementation has been based on Numerical Recipes in C paragraph 14.6.
xvalues
 The array with the xvalues.yvalues
 The array with the yvalues.
public static double spearmanCorrelationS(double[] xvalues, double[] yvalues)
public static double factorialln(int n)
gammaln(double)
method, which is highly optimized.
n
 The nonnegative integer.
public static double binomialln(int n, int k)
n
 The nonnegative integer.k
 The nonnegative integer.
public static double ttest(double[] a, double[] b)
a
 Population 1.b
 Population 2.
public static double ftest(double[] a, double[] b)
a
 Population 1.b
 Population 2.
public static double[] rank(double[] data, boolean reversed)
A binary search is utilized to find the rankvalues of each of the cells.
data
 The data vector to rank.reversed
 When set to true, the ranks will be reversed
public static double[][] rank(double[][] data, boolean reversed, int rowcolumn) throws java.lang.IllegalArgumentException
A binary search is utilized to find the rankvalues of each of the cells.
data
 The datamatrix to rankreversed
 When set to true, the ranks will be reversedrowcolumn
 Either ROW
or COLUMN
java.lang.IllegalArgumentException
public static final void qsort(double[] values, double[]... arrays)
values
 arrays
 public static double[] permute(double[] vector)
vector
 The vector which needs to be permuted.
public static double[][] permute(double[][] data, int rowcolumn) throws java.lang.IllegalArgumentException
ROW
or COLUMN
. This method makes
use of an internally seeded with time of creation for this class. This should ensure
that the pseudo random values generated are reasonable. The passed matrix is not
affected.
data
 The matrix to be permuted.rowcolumn
 Either ROW
or COLUMN
java.lang.IllegalArgumentException
 Thrown when the rowcolumn parameter has an illegal valuepublic static double gammaln(double z)
Reference: "Lanczos, C. 'A precision approximation of the gamma function', J. SIAM Numer. Anal., B, 1, 8696, 1964.". Translation of Alan Miller's FORTRANimplementation.
z
 The value for which to calculate the gammaln.
http://lib.stat.cmu.edu/apstat/245
public static double beta(double z, double w)
public static double betai(double a, double b, double x)
public static double betacf(double a, double b, double x)
public static double[] shapiroWilk(double[] values) throws java.lang.IllegalArgumentException
values
 The distribution to test.
SHAPIRO_WILK_PVALUE
and SHAPIRO_WILK_WSTAT
).
java.lang.IllegalArgumentException
 Thrown when the length of the vector is less than 3 elements.public static double durbinWatson(double[] values)
The residual e is calculated by subtracting the measured value from the mean of all the values.
values
 The array with the values.
public static double durbinWatsonCERN(double[] values)
values



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