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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.StudentDist
public class StudentDist
Extends the class ContinuousDistribution
for
the Student-t distribution
with n degrees of freedom, where n is a positive integer.
Its density is
GammaDist
.
The non-static methods cdf
and barF
use
the same algorithm as in cdf
.
Field Summary |
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Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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decPrec |
Constructor Summary | |
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StudentDist(int n)
Constructs a StudentDist object with n degrees of freedom. |
Method Summary | |
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static double |
barF(int n,
double x)
Computes the complementary distribution function bar(F)(x). |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(int n,
double x)
Returns an approximation for the Student-t distribution function with n degrees of freedom. |
static double |
cdf2(int n,
int d,
double x)
Returns an approximation of the Student-t distribution function with n degrees of freedom. |
double |
density(double x)
Returns f (x), the density of X evaluated at x. |
static double |
density(int n,
double x)
Computes the density function for a Student-t distribution with n degrees of freedom. |
static StudentDist |
getInstanceFromMLE(double[] x,
int m)
Creates a new instance of a Student-t distribution with parameter n estimated using the maximum likelihood method based on the m observations in table x[i], i = 0, 1,…, m - 1. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int m)
Estimates and returns the parameter [hat(n)] of the Student-t distribution using the maximum likelihood method based on the m observations in table x[i], i = 0, 1,…, m - 1. |
double |
getMean()
Returns the mean of the distribution function. |
static double |
getMean(int n)
Returns the mean E[X] = 0 of the Student-t distribution with parameter n. |
int |
getN()
Returns the parameter n associated with this object. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(int n)
Computes and returns the standard deviation of the Student-t distribution with parameter n. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(int n)
Computes and returns the variance Var[X] = n/(n - 2) of the Student-t distribution with parameter n. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
static double |
inverseF(int n,
double u)
Returns an approximation of F-1(u), where F is the Student-t distribution function with n degrees of freedom. |
void |
setN(int n)
Sets the parameter n associated with this object. |
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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barF, inverseBisection, inverseBrent |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public StudentDist(int n)
Method Detail |
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public double density(double x)
ContinuousDistribution
density
in class ContinuousDistribution
x
- value at which the density is evaluated
public double cdf(double x)
Distribution
x
- value at which the distribution function is evaluated
public double inverseF(double u)
Distribution
inverseF
in interface Distribution
inverseF
in class ContinuousDistribution
u
- value in the interval (0, 1) for which the inverse
distribution function is evaluated
public double getMean()
Distribution
public double getVariance()
Distribution
public double getStandardDeviation()
Distribution
public static double density(int n, double x)
public static double cdf(int n, double x)
public static double cdf2(int n, int d, double x)
2F(x) = | In/2, 1/2(n/(n + x2)) | for x < 0, |
2F(x) = | I1/2, n/2(x2/(n + x2)) | for x >= 0, |
BetaDist
, which is approximated by calling
BetaDist.cdf
.
The function tries to return d decimals digits of precision
(but there is no guarantee).
This method is much slower (twenty to forty times, depending on parameters)
than cdf, but could be used if precision is important.
public static double barF(int n, double x)
public static double inverseF(int n, double u)
public static StudentDist getInstanceFromMLE(double[] x, int m)
x
- the list of observations to use to evaluate parametersm
- the number of observations to use to evaluate parameterspublic static double[] getMaximumLikelihoodEstimate(double[] x, int m)
x
- the list of observations to use to evaluate parametersm
- the number of observations to use to evaluate parameters
public static double getMean(int n)
public static double getVariance(int n)
public static double getStandardDeviation(int n)
public int getN()
public void setN(int n)
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