jdistlib

Class NonCentralT

java.lang.Object

jdistlib.generic.GenericDistribution

jdistlib.NonCentralT

public class NonCentralT
extends jdistlib.generic.GenericDistribution

Field Summary

Fields

Modifier and Type	Field and Description
protected double	df
protected double	ncp

Fields inherited from class jdistlib.generic.GenericDistribution

random

Constructor Summary

Constructors

Constructor and Description
NonCentralT(double df, double ncp)

Method Summary

Modifier and Type	Method and Description
double	cumulative(double p, boolean lower_tail, boolean log_p)
static double	cumulative(double t, double df, double ncp, boolean lower_tail, boolean log_p)
double	density(double x, boolean log)
static double	density(double x, double df, double ncp, boolean give_log) From Johnson, Kotz and Balakrishnan (1995) [2nd ed.; formula (31.15), p.516], the non-central t density is f(x, df, ncp) = exp(-.5*ncp^2) * gamma((df+1)/2) / (sqrt(pi*df)* gamma(df/2)) * (df/(df+x^2))^((df+1)/2) * sum_{j=0}^Inf gamma((df+j+1)/2)/(factorial(j)* gamma((df+1)/2)) * (x*ncp*sqrt(2)/sqrt(df+x^2))^ j 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 !
double	quantile(double q, boolean lower_tail, boolean log_p)
static double	quantile(double p, double df, double ncp, boolean lower_tail, boolean log_p)
double	random()
static double	random(double df, double ncp, jdistlib.rng.RandomEngine random)
static double[]	random(int n, double df, double ncp, jdistlib.rng.RandomEngine random)

Methods inherited from class jdistlib.generic.GenericDistribution

cumulative_hazard, cumulative_hazard, cumulative, cumulative, cumulative, density, density, getRandomEngine, hazard, hazard, inverse_survival, inverse_survival, quantile, quantile, quantile, random, random, setRandomEngine, survival, survival, survival

Methods inherited from class java.lang.Object

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

Field Detail

df

protected double df

ncp

protected double ncp

Constructor Detail

NonCentralT

public NonCentralT(double df,
                   double ncp)

Method Detail

density

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

    From Johnson, Kotz and Balakrishnan (1995) [2nd ed.; formula (31.15), p.516],
    the non-central t density is

      f(x, df, ncp) =

        exp(-.5*ncp^2) * gamma((df+1)/2) / (sqrt(pi*df)* gamma(df/2)) * (df/(df+x^2))^((df+1)/2) *
          sum_{j=0}^Inf  gamma((df+j+1)/2)/(factorial(j)* gamma((df+1)/2)) * (x*ncp*sqrt(2)/sqrt(df+x^2))^ j


    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.

 FIXME: pnt() is known to be inaccurate in the (very) left tail and for ncp > 38
       ==> use a direct log-space summation formula in that case         * 

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,
                                  jdistlib.rng.RandomEngine random)

random

public static final double[] random(int n,
                                    double df,
                                    double ncp,
                                    jdistlib.rng.RandomEngine random)

density

public double density(double x,
                      boolean log)

Specified by:

density in class jdistlib.generic.GenericDistribution

cumulative

public double cumulative(double p,
                         boolean lower_tail,
                         boolean log_p)

Specified by:

cumulative in class jdistlib.generic.GenericDistribution

quantile

public double quantile(double q,
                       boolean lower_tail,
                       boolean log_p)

Specified by:

quantile in class jdistlib.generic.GenericDistribution

random

public double random()

Specified by:

random in class jdistlib.generic.GenericDistribution