public class NonCentralT extends Object
| Constructor and Description |
|---|
NonCentralT() |
| 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) |
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.
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,
QRandomEngine random)
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