rvl.stat.dist
Class T

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

public class T

extends java.lang.Object

Functions relating to the t distribution (central and noncentral)

Constructor Summary

T()

Method Summary

static double	cdf(double t, double df)
static double	cdf(double t, double df, double delta)
static double	delta(double power, double df, int tail, double alpha)
static double	power(double alpha)
static double	power(double delta, double df, int tail, double alpha)
static double	powerEquiv(double alpha) Used for integration in rocEquiv -- not meant to be called by user
static double	powerEquiv(double mu, double tol, double se, double df, double alpha)
static double	quantile(double p, double df)
static double	quantile(double p, double df, double delta)
static double	rocArea(double delta, double df, int tail)
static double	rocArea(double delta, double df, int tail, double eps)
static double	rocEquiv(double mu, double tol, double se, double df)
static double	rocEquiv(double mu, double tol, double se, double df, double eps)

Methods inherited from class java.lang.Object

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

Constructor Detail

T

public T()

Method Detail

cdf

public static double cdf(double t,
                         double df,
                         double delta)

Returns:

noncentral cdf at t with d.f. df and noncentrality parameter delta

cdf

public static double cdf(double t,
                         double df)

Returns:

central cdf at t with d.f. df

quantile

public static double quantile(double p,
                              double df,
                              double delta)

Returns:

pth quantile of the noncentral t with d.f. df and noncentrality parameter delta

quantile

public static double quantile(double p,
                              double df)

power

public static double power(double delta,
                           double df,
                           int tail,
                           double alpha)

Returns:

power of normal-theory t test of H₀: delta = 0 vs H₁: delta = delta with d.f. df and size level alpha. tail is ( <0 | ==0 | >0 ) for a (left | two | right)-tailed test.

delta

public static double delta(double power,
                           double df,
                           int tail,
                           double alpha)

rocArea

public static double rocArea(double delta,
                             double df,
                             int tail,
                             double eps)

Parameters:

eps - Bound on the error of numerical integration

Returns:

area under the ROC curve with ncp delta and d.f. df This is the integral of power(..., alpha) over alpha.

rocArea

public static double rocArea(double delta,
                             double df,
                             int tail)

Returns:

rocArea(delta, df, 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

powerEquiv

public static double powerEquiv(double mu,
                                double tol,
                                double se,
                                double df,
                                double alpha)

Returns:

power of test of equivalence when the true mean is mu, the tolerance bound for a negligible effect is tol, the population value of the standard error is , degrees ofse, degrees of freedom df, and significance level alpha.

Uses a crude trapezoidal-rule integration over 100 subintervals

powerEquiv

public static double powerEquiv(double alpha)

Used for integration in rocEquiv -- not meant to be called by user

rocEquiv

public static double rocEquiv(double mu,
                              double tol,
                              double se,
                              double df,
                              double eps)

Returns:

ROC area for an equivalence test

rocEquiv

public static double rocEquiv(double mu,
                              double tol,
                              double se,
                              double df)

Returns:

ROC area for an equivalence test, with eps = 1e-4