Package jdistlib

Class NonCentralT

java.lang.Object

jdistlib.generic.GenericDistribution

jdistlib.NonCentralT

public class NonCentralT
extends GenericDistribution

Field Summary

Fields

Modifier and Type	Field	Description
protected double	df
protected double	ncp

Fields inherited from class jdistlib.generic.GenericDistribution

random

Constructor Summary

Constructors

Constructor	Description
NonCentralT(double df, double ncp)

Method Summary

Modifier and Type	Method	Description
double	cumulative(double p, boolean lower_tail, boolean log_p)
static final double	cumulative(double t, double df, double ncp, boolean lower_tail, boolean log_p)
double	density(double x, boolean log)
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) = 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.
double	quantile(double q, boolean lower_tail, boolean log_p)
static final double	quantile(double p, double df, double ncp, boolean lower_tail, boolean log_p)
double	random()
static final double	random(double df, double ncp, RandomEngine random)
static final double[]	random(int n, double df, double ncp, RandomEngine random)

Methods inherited from class jdistlib.generic.GenericDistribution

copyBackward, cumulative, cumulative, cumulative, cumulative_hazard, cumulative_hazard, cumulativeInto, density, density, densityInto, getRandomEngine, hazard, hazard, inverse_survival, inverse_survival, quantile, quantile, quantile, quantileInto, random, random, randomInto, setRandomEngine, survival, survival, survival

Methods inherited from class java.lang.Object

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

Field Details

df

protected double df

ncp

protected double ncp

Constructor Details

NonCentralT

public NonCentralT(double df,
 double ncp)

Method Details

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) =
            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,
 RandomEngine random)

random

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

density

public double density(double x,
 boolean log)

Specified by:

density in class GenericDistribution

cumulative

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

Specified by:

cumulative in class GenericDistribution

quantile

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

Specified by:

quantile in class GenericDistribution

random

public double random()

Specified by:

random in class GenericDistribution