rvl.stat.dist
Class Normal

java.lang.Object
  |
  +--rvl.stat.dist.Normal

public class Normal

extends java.lang.Object

The normal distribution

Constructor Summary

Normal()

Method Summary

static double	cdf(double z)
static double	cdf(double x, double mu, double sigma)
static double	effectSize(double goal, int tail, double alpha) Effect size of a test based on the normal distribution
static double	pdf(double z)
static double	power(double alpha)
static double	power(double mu1, int tail, double alpha) Power for homogeneous-variance case
static double	power(double mu1, int tail, double alpha, double sigma1)
static double	quantile(double p)
static double	quantile(double p, double mu, double sigma)
static double	rocArea(double mu1, int tail)
static double	rocArea(double mu1, int tail, double eps)

Methods inherited from class java.lang.Object

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

Constructor Detail

Normal

public Normal()

Method Detail

cdf

public static double cdf(double z)

Returns:

standard normal cdf at z

pdf

public static double pdf(double z)

Returns:

density at z of standard normal distribution

quantile

public static double quantile(double p)

Returns:

standard normal quantile at p

cdf

public static double cdf(double x,
                         double mu,
                         double sigma)

Returns:

cdf at x of N(mu,sigma) distribution

quantile

public static double quantile(double p,
                              double mu,
                              double sigma)

Returns:

pth quantile of N(mu,sigma) distribution

power

public static double power(double mu1,
                           int tail,
                           double alpha,
                           double sigma1)

Returns:

power of normal-theory test of H₀: mu = 0 where sigma0 = 1 and the distribution under H₁ is N(mu1, sigma1)

power

public static double power(double mu1,
                           int tail,
                           double alpha)

Power for homogeneous-variance case

Returns:

power(mu1, tail, alpha, 1.0)

effectSize

public static double effectSize(double goal,
                                int tail,
                                double alpha)

Effect size of a test based on the normal distribution

Returns:

value of mu1 such that power(mu1, tail, alpha) == goal

See Also:

power(double, int, double, double)

rocArea

public static double rocArea(double mu1,
                             int tail,
                             double eps)

Parameters:

eps - Bound on the error of numerical integration

Returns:

area under the ROC curve with effect size mu1. This is the integral of power(mu1, tail, alpha) over alpha.

rocArea

public static double rocArea(double mu1,
                             int tail)

Returns:

rocArea(mu1, tail, 1e-4)

power

public static double power(double alpha)

Returns:

power at alpha for internally stored parameters. This is an auxiliary function used by rocArea, not intended for other uses