public class NonCentralT extends GenericDistribution
| Constructor and Description |
|---|
NonCentralT(double df,
double ncp) |
| 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) =
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 double |
quantile(double p,
double df,
double ncp,
boolean lower_tail,
boolean log_p) |
double |
random() |
static double |
random(double df,
double ncp,
RandomEngine random) |
static double[] |
random(int n,
double df,
double ncp,
RandomEngine random) |
cumulative_hazard, cumulative_hazard, cumulative, cumulative, cumulative, density, density, getRandomEngine, hazard, hazard, inverse_survival, inverse_survival, quantile, quantile, quantile, random, random, setRandomEngine, survival, survival, survivalpublic 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.
public static final double cumulative(double t,
double df,
double ncp,
boolean lower_tail,
boolean log_p)
public static final double quantile(double p,
double df,
double ncp,
boolean lower_tail,
boolean log_p)
public static final double random(double df,
double ncp,
RandomEngine random)
public static final double[] random(int n,
double df,
double ncp,
RandomEngine random)
public double density(double x,
boolean log)
density in class GenericDistributionpublic double cumulative(double p,
boolean lower_tail,
boolean log_p)
cumulative in class GenericDistributionpublic double quantile(double q,
boolean lower_tail,
boolean log_p)
quantile in class GenericDistributionpublic double random()
random in class GenericDistribution