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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.ChiDist
public class ChiDist
Extends the class ContinuousDistribution
for the chi
distribution with shape parameter
v > 0, where the number of degrees of freedom
v is a positive integer.
The density function is given by
GammaDist
.
The distribution function is
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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ChiDist(int nu)
Constructs a ChiDist object. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
static double |
barF(int nu,
double x)
Computes the complementary distribution. |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(int nu,
double x)
Computes the distribution function by using the gamma distribution function. |
double |
density(double x)
Returns f (x), the density of X evaluated at x. |
static double |
density(int nu,
double x)
Computes the density function. |
static ChiDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a chi distribution with parameter ν estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int n)
Estimates and returns the parameter [hat(ν)] of the chi distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
double |
getMean()
Returns the mean of the distribution function. |
static double |
getMean(int nu)
Computes and returns the mean of the chi distribution with parameter ν. |
int |
getNu()
Returns the value of ν for this object. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(int nu)
Computes and returns the standard deviation of the chi distribution with parameter ν. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(int nu)
Computes and returns the variance of the chi distribution with parameter ν. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
static double |
inverseF(int nu,
double u)
Returns the inverse distribution function computed using the gamma inversion. |
void |
setNu(int nu)
Sets the value of ν for this object. |
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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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 ChiDist(int nu)
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 barF(double x)
Distribution
barF
in interface Distribution
barF
in class ContinuousDistribution
x
- value at which the complementary 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 nu, double x)
public static double cdf(int nu, double x)
public static double barF(int nu, double x)
public static double inverseF(int nu, double u)
public static ChiDist getInstanceFromMLE(double[] x, int n)
x
- the list of observations to use to evaluate parametersn
- the number of observations to use to evaluate parameterspublic static double[] getMaximumLikelihoodEstimate(double[] x, int n)
x
- the list of observations to use to evaluate parametersn
- the number of observations to use to evaluate parameters
public static double getMean(int nu)
public static double getVariance(int nu)
public static double getStandardDeviation(int nu)
public int getNu()
public void setNu(int nu)
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