Statistics

java.lang.Object
- jhplot.stat.Statistics

```
public class Statistics
extends Object
```
A static class for statistical calculations.

Constructor Summary

Constructors
Constructor and Description

Statistics()

Constructors
Constructor and Description
`Statistics()`

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`static double[][]`	`correlation(double[][] v)` Correlation
`static double[][]`	`correlation(double[][] v1, double[][] v2)` Correlation coefficient, covariance(v1, v2) / Math.sqrt(variance(v1) * variance(v2)
`static double`	`correlation(double[] v1, double[] v2)` Correlation coefficient, covariance(v1, v2) / Math.sqrt(variance(v1) * variance(v2)
`static double[][]`	`covariance(double[][] v)` Covariance
`static double[][]`	`covariance(double[][] v1, double[][] v2)` Covariance
`static double`	`covariance(double[] v1, double[] v2)` Covariance
`void`	`doc()` Show online documentation.
`static double`	`FProbability(double F, int df1, int df2)` Computes probability of F-ratio.
`static double`	`gamma(double x)` Returns the Gamma function of the argument.
`static double`	`incompleteBeta(double aa, double bb, double xx)` Returns the Incomplete Beta Function evaluated from zero to `xx`.
`static double`	`incompleteBetaFraction1(double a, double b, double x)` Continued fraction expansion #1 for incomplete beta integral.
`static double`	`incompleteBetaFraction2(double a, double b, double x)` Continued fraction expansion #2 for incomplete beta integral.
`static double`	`lnGamma(double x)` Returns natural logarithm of gamma function.
`static double`	`mean(double[] v)` Get mean value
`static double[]`	`mean(double[][] v)` Get mean
`static double`	`p1evl(double x, double[] coef, int N)` Evaluates the given polynomial of degree `N` at `x`.
`static double`	`polevl(double x, double[] coef, int N)` Evaluates the given polynomial of degree `N` at `x`.
`static double`	`powerSeries(double a, double b, double x)` Power series for incomplete beta integral.
`static double`	`stddeviation(double[] v)` Standard deviation
`static double[]`	`stddeviation(double[][] v)` Standard deviation
`static double`	`stirlingFormula(double x)` Returns the Gamma function computed by Stirling's formula.
`static double`	`variance(double[] v)` Variance
`static double[]`	`variance(double[][] v)` Variance

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

- Constructor Detail
  - Statistics
```
public Statistics()
```
- Method Detail
  - mean
```
public static double mean(double[] v)
```
    Get mean value
    
    Parameters:
    
    v - vector
  - mean
```
public static double[] mean(double[][] v)
```
    Get mean
    
    Parameters:
    
    v - 2D array
    
    Returns:
  - stddeviation
```
public static double stddeviation(double[] v)
```
    Standard deviation
    
    Parameters:
    
    v - vector
    
    Returns:
  - variance
```
public static double variance(double[] v)
```
    Variance
    
    Parameters:
    
    v -
    
    Returns:
    
    vector
  - stddeviation
```
public static double[] stddeviation(double[][] v)
```
    Standard deviation
    
    Parameters:
    
    v -
    
    Returns:
  - variance
```
public static double[] variance(double[][] v)
```
    Variance
    
    Parameters:
    
    v - vector
    
    Returns:
  - covariance
```
public static double covariance(double[] v1,
                                double[] v2)
```
    Covariance
    
    Parameters:
    
    v1 - first vector
    
    v2 - second vector
    
    Returns:
  - covariance
```
public static double[][] covariance(double[][] v1,
                                    double[][] v2)
```
    Covariance
    
    Parameters:
    
    v1 - first 2D array
    
    v2 - second 2D array
    
    Returns:
  - covariance
```
public static double[][] covariance(double[][] v)
```
    Covariance
    
    Parameters:
    
    v -
    
    Returns:
  - correlation
```
public static double correlation(double[] v1,
                                 double[] v2)
```
    Correlation coefficient, covariance(v1, v2) / Math.sqrt(variance(v1) * variance(v2)
    
    Parameters:
    
    v1 - first vector
    
    v2 - second vector
    
    Returns:
  - correlation
```
public static double[][] correlation(double[][] v1,
                                     double[][] v2)
```
    Correlation coefficient, covariance(v1, v2) / Math.sqrt(variance(v1) * variance(v2)
    
    Parameters:
    
    v1 - first vector
    
    v2 - second vector
    
    Returns:
  - correlation
```
public static double[][] correlation(double[][] v)
```
    Correlation
    
    Parameters:
    
    v -
    
    Returns:
  - FProbability
```
public static double FProbability(double F,
                                  int df1,
                                  int df2)
```
    Computes probability of F-ratio.
    
    Parameters:
    
    F - the F-ratio
    
    df1 - the first number of degrees of freedom
    
    df2 - the second number of degrees of freedom
    
    Returns:
    
    the probability of the F-ratio.
  - incompleteBeta
```
public static double incompleteBeta(double aa,
                                    double bb,
                                    double xx)
```
    Returns the Incomplete Beta Function evaluated from zero to xx.
    
    Parameters:
    
    aa - the alpha parameter of the beta distribution.
    
    bb - the beta parameter of the beta distribution.
    
    xx - the integration end point.
  - powerSeries
```
public static double powerSeries(double a,
                                 double b,
                                 double x)
```
    Power series for incomplete beta integral. Use when b*x is small and x not too close to 1.
  - lnGamma
```
public static double lnGamma(double x)
```
    Returns natural logarithm of gamma function.
    
    Parameters:
    
    x - the value
    
    Returns:
    
    natural logarithm of gamma function
  - p1evl
```
public static double p1evl(double x,
                           double[] coef,
                           int N)
```
    Evaluates the given polynomial of degree N at x. Evaluates polynomial when coefficient of N is 1.0. Otherwise same as polevl().
```
                     2          N
 y  =  C  + C x + C x  +...+ C x
        0    1     2          N
 
 Coefficients are stored in reverse order:
 
 coef[0] = C  , ..., coef[N] = C  .
            N                   0
 
```
    The function p1evl() assumes that coef[N] = 1.0 and is omitted from the array. Its calling arguments are otherwise the same as polevl().
    In the interest of speed, there are no checks for out of bounds arithmetic.
    Parameters:
    
    x - argument to the polynomial.
    
    coef - the coefficients of the polynomial.
    
    N - the degree of the polynomial.
  - gamma
```
public static double gamma(double x)
```
    Returns the Gamma function of the argument.
  - stirlingFormula
```
public static double stirlingFormula(double x)
```
    Returns the Gamma function computed by Stirling's formula. The polynomial STIR is valid for 33 <= x <= 172.
  - polevl
```
public static double polevl(double x,
                            double[] coef,
                            int N)
```
    Evaluates the given polynomial of degree N at x.
```
                     2          N
 y  =  C  + C x + C x  +...+ C x
        0    1     2          N
 
 Coefficients are stored in reverse order:
 
 coef[0] = C  , ..., coef[N] = C  .
            N                   0
 
```
    In the interest of speed, there are no checks for out of bounds arithmetic.
    Parameters:
    
    x - argument to the polynomial.
    
    coef - the coefficients of the polynomial.
    
    N - the degree of the polynomial.
  - incompleteBetaFraction1
```
public static double incompleteBetaFraction1(double a,
                                             double b,
                                             double x)
```
    Continued fraction expansion #1 for incomplete beta integral.
  - incompleteBetaFraction2
```
public static double incompleteBetaFraction2(double a,
                                             double b,
                                             double x)
```
    Continued fraction expansion #2 for incomplete beta integral.
  - doc
```
public void doc()
```
    Show online documentation.

Class Statistics

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Statistics

Method Detail

mean

mean

stddeviation

variance

stddeviation

variance

covariance

covariance

covariance

correlation

correlation

correlation

FProbability

incompleteBeta

powerSeries

lnGamma

p1evl

gamma

stirlingFormula

polevl

incompleteBetaFraction1

incompleteBetaFraction2

doc