DiscreteStatistics

java.lang.Object
- pal.statistics.DiscreteStatistics

```
public class DiscreteStatistics
extends java.lang.Object
```
simple discrete statistics (mean, variance, cumulative probability, quantiles etc.)

Version:

$Id: DiscreteStatistics.java,v 1.5 2001/07/13 14:39:13 korbinian Exp $

Author:

Korbinian Strimmer

Constructor Summary

Constructors
Constructor and Description

DiscreteStatistics()

Constructors
Constructor and Description
`DiscreteStatistics()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`cdf(double z, double[] x)` compute the cumulative probability Pr(x <= z) for a given z and a distribution of x
`static double`	`cdf(double z, double[] x, int[] indices)` compute the cumulative probability Pr(x <= z) for a given z and a distribution of x
`static double`	`mean(double[] x)` compute mean
`static double`	`quantile(double q, double[] x)` compute the q-th quantile for a distribution of x (= inverse cdf)
`static double`	`quantile(double q, double[] x, int[] indices)` compute the q-th quantile for a distribution of x (= inverse cdf)
`static double`	`skewness(double[] x)` compute fisher skewness
`static double`	`stdev(double[] x)` compute standard deviation
`static double`	`variance(double[] x)` compute variance (ML estimator)
`static double`	`variance(double[] x, double mean)` compute variance (ML estimator)
`static double`	`varianceSampleMean(double[] x)` compute variance of sample mean (ML estimator)
`static double`	`varianceSampleMean(double[] x, double mean)` compute variance of sample mean (ML estimator)

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

- Constructor Detail
  - DiscreteStatistics
```
public DiscreteStatistics()
```
- Method Detail
  - mean
```
public static double mean(double[] x)
```
    compute mean
    
    Parameters:
    
    x - list of numbers
    
    Returns:
    
    mean
  - variance
```
public static double variance(double[] x,
                              double mean)
```
    compute variance (ML estimator)
    
    Parameters:
    
    x - list of numbers
    
    mean - assumed mean of x
    
    Returns:
    
    variance of x (ML estimator)
  - skewness
```
public static double skewness(double[] x)
```
    compute fisher skewness
    
    Parameters:
    
    x - list of numbers
    
    Returns:
    
    skewness of x
  - stdev
```
public static double stdev(double[] x)
```
    compute standard deviation
    
    Parameters:
    
    x - list of numbers
    
    Returns:
    
    standard deviation of x
  - variance
```
public static double variance(double[] x)
```
    compute variance (ML estimator)
    
    Parameters:
    
    x - list of numbers
    
    Returns:
    
    variance of x (ML estimator)
  - varianceSampleMean
```
public static double varianceSampleMean(double[] x,
                                        double mean)
```
    compute variance of sample mean (ML estimator)
    
    Parameters:
    
    x - list of numbers
    
    mean - assumed mean of x
    
    Returns:
    
    variance of x (ML estimator)
  - varianceSampleMean
```
public static double varianceSampleMean(double[] x)
```
    compute variance of sample mean (ML estimator)
    
    Parameters:
    
    x - list of numbers
    
    Returns:
    
    variance of x (ML estimator)
  - quantile
```
public static double quantile(double q,
                              double[] x,
                              int[] indices)
```
    compute the q-th quantile for a distribution of x (= inverse cdf)
    
    Parameters:
    
    q - quantile (0 < q <= 1)
    
    x - discrete distribution (an unordered list of numbers)
    
    indices - index sorting x
    
    Returns:
    
    q-th quantile
  - quantile
```
public static double quantile(double q,
                              double[] x)
```
    compute the q-th quantile for a distribution of x (= inverse cdf)
    
    Parameters:
    
    q - quantile (0 <= q <= 1)
    
    x - discrete distribution (an unordered list of numbers)
    
    Returns:
    
    q-th quantile
  - cdf
```
public static double cdf(double z,
                         double[] x,
                         int[] indices)
```
    compute the cumulative probability Pr(x <= z) for a given z and a distribution of x
    
    Parameters:
    
    z - threshold value
    
    x - discrete distribution (an unordered list of numbers)
    
    indices - index sorting x
    
    Returns:
    
    cumulative probability
  - cdf
```
public static double cdf(double z,
                         double[] x)
```
    compute the cumulative probability Pr(x <= z) for a given z and a distribution of x
    
    Parameters:
    
    z - threshold value
    
    x - discrete distribution (an unordered list of numbers)
    
    Returns:
    
    cumulative probability

Class DiscreteStatistics

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

DiscreteStatistics

Method Detail

mean

variance

skewness

stdev

variance

varianceSampleMean

varianceSampleMean

quantile

quantile

cdf

cdf