vec_math
Class IntegerMoments

java.lang.Object
  vec_math.IntegerMoments

public class IntegerMoments
extends Object

Moments is a stastistic package that allows calculation of sample central moments of discrete samples. They are defined as

   M_k=1/n·Σ(x_i-μ)^k,
   

where μ is the sample mean and the summing is done over all smaple values x_i. The connection to the power sums S_k=Σx_i^k is

   M_k=Σ_0^n (-1)^(n-k)(n over k) 1/N(n-k+1)S_k*S_1^(n-k)
   

Note that sample moments are not identically to population moments, for the first moments, the following similarites hold

   μ=M_1
   μ_2=σ²=N/(N-1)·M_2 (μ_2=population variance)
   μ_3=N²/[(N-1)(N-2)]·M_3 
   μ_4=N²[(N+1)M_4-3(N-1)M_2²]/[(N-1)(N-2)(N-3)+3N/(N-1)M_2 
   

To normalize the moments, they are devided by the k/2-th power of the sample variance (roughly the k-th power of the standard deviation).

Nested Class Summary

static class

IntegerMoments.FitsMoments Grabs a fits file and displays the moments up to the order given in the optional second command line argument.

Field Summary

private long	n The number of values in the sample.
private int	order The order of the moments, defined at construction.
private static int	ORDER Default order number.
private BigInteger[]	power The cummulated power sums.

Constructor Summary

IntegerMoments()
Constructs a new moments object.

IntegerMoments(int k)
Constructs a new moments object.

Method Summary

void	addValue(int xi) Adds a raw value.
double	getAverage() Returns the sample average, which is equal to the first raw moment.
int	getOrder() Gets the order.
double	getRawMoment(int k) Returns the k-th sample raw moment, which is 1/N times the power sum.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

ORDER

private static final int ORDER

Default order number.

See Also:

Constant Field Values

order

private int order

The order of the moments, defined at construction.

power

private BigInteger[] power

The cummulated power sums. Index equals power minus one.

n

private long n

The number of values in the sample.

Constructor Detail

IntegerMoments

public IntegerMoments()

Constructs a new moments object. Defaults the order to four.

IntegerMoments

public IntegerMoments(int k)

Constructs a new moments object. Moments available to the order specified here.

Method Detail

getOrder

public int getOrder()

Gets the order.

addValue

public void addValue(int xi)

Adds a raw value. Updates all power sums accordingly.

getAverage

public double getAverage()

Returns the sample average, which is equal to the first raw moment.

getRawMoment

public double getRawMoment(int k)

Returns the k-th sample raw moment, which is 1/N times the power sum.