jdistlib

Class NonCentralT

java.lang.Object

jdistlib.NonCentralT

public class NonCentralT
extends Object

Constructor Summary

Constructors

Constructor and Description
NonCentralT()

Method Summary

Methods

Modifier and Type	Method and Description
static double	cumulative(double t, double df, double ncp, boolean lower_tail, boolean log_p)
static double	density(double x, double df, double ncp, boolean give_log) The non-central t density is f(x, df, ncp) = df^(df/2) * exp(-.5*ncp^2) / (sqrt(pi)*gamma(df/2)*(df+x^2)^((df+1)/2)) * sum_{k=0}^Inf gamma((df + k + df)/2)*ncp^k / prod(1:k)*(2*x^2/(df+x^2))^(k/2) The functional relationship f(x, df, ncp) = df/x * (F(sqrt((df+2)/df)*x, df+2, ncp) - F(x, df, ncp)) is used to evaluate the density at x !
static double	quantile(double p, double df, double ncp, boolean lower_tail, boolean log_p)
static double	random(double df, double ncp, QRandomEngine random)

Methods inherited from class java.lang.Object

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

Constructor Detail

NonCentralT

public NonCentralT()

Method Detail

density

public static final double density(double x,
             double df,
             double ncp,
             boolean give_log)

    The non-central t density is

           f(x, df, ncp) =
                df^(df/2) * exp(-.5*ncp^2) /
                (sqrt(pi)*gamma(df/2)*(df+x^2)^((df+1)/2)) *
                sum_{k=0}^Inf  gamma((df + k + df)/2)*ncp^k /
                                prod(1:k)*(2*x^2/(df+x^2))^(k/2)

    The functional relationship

           f(x, df, ncp) = df/x *
                              (F(sqrt((df+2)/df)*x, df+2, ncp) - F(x, df, ncp))

    is used to evaluate the density at x != 0 and

           f(0, df, ncp) = exp(-.5*ncp^2) /
                                (sqrt(pi)*sqrt(df)*gamma(df/2))*gamma((df+1)/2)

    is used for x=0.

    All calculations are done on log-scale to increase stability.
 

cumulative

public static final double cumulative(double t,
                double df,
                double ncp,
                boolean lower_tail,
                boolean log_p)

quantile

public static final double quantile(double p,
              double df,
              double ncp,
              boolean lower_tail,
              boolean log_p)

random

public static final double random(double df,
            double ncp,
            QRandomEngine random)