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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.CauchyDist
public class CauchyDist
Extends the class ContinuousDistribution for
the Cauchy distribution
with location parameter α
and scale parameter β > 0.
The density function is given by
| Field Summary |
|---|
| Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
|---|
decPrec |
| Constructor Summary | |
|---|---|
CauchyDist()
Constructs a CauchyDist object with parameters α = 0 and β = 1. |
|
CauchyDist(double alpha,
double beta)
Constructs a CauchyDist object with parameters α = alpha and β = beta. |
|
| Method Summary | |
|---|---|
double |
barF(double x)
Returns the complementary distribution function. |
static double |
barF(double alpha,
double beta,
double x)
Computes the complementary distribution. |
double |
cdf(double x)
Returns the distribution function F(x). |
static double |
cdf(double alpha,
double beta,
double x)
Computes the distribution function. |
double |
density(double x)
Returns f (x), the density evaluated at x. |
static double |
density(double alpha,
double beta,
double x)
Computes the density function. |
double |
getAlpha()
Returns the value of α for this object. |
double |
getBeta()
Returns the value of β for this object. |
static CauchyDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a Cauchy distribution with parameters α and β estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1. |
double |
getMean()
Returns the mean. |
static double |
getMean(double alpha,
double beta)
Throws an exception since the mean does not exist. |
static double[] |
getMLE(double[] x,
int n)
Estimates the parameters (α, β) of the Cauchy distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. |
double[] |
getParams()
Return a table containing parameters of the current distribution. |
double |
getStandardDeviation()
Returns the standard deviation. |
static double |
getStandardDeviation(double alpha,
double beta)
Returns ∞ since the standard deviation does not exist. |
double |
getVariance()
Returns the variance. |
static double |
getVariance(double alpha,
double beta)
Returns ∞ since the variance does not exist. |
double |
inverseF(double u)
Returns the inverse distribution function x = F-1(u). |
static double |
inverseF(double alpha,
double beta,
double u)
Computes the inverse of the distribution. |
void |
setParams(double alpha,
double beta)
Sets the value of the parameters α and β for this object. |
String |
toString()
|
| Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
|---|
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup |
| Methods inherited from class java.lang.Object |
|---|
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait |
| Constructor Detail |
|---|
public CauchyDist()
public CauchyDist(double alpha,
double beta)
| Method Detail |
|---|
public double density(double x)
ContinuousDistribution
density in class ContinuousDistributionx - 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)
ContinuousDistribution
barF in interface DistributionbarF in class ContinuousDistributionx - value at which the complementary distribution function is evaluated
public double inverseF(double u)
ContinuousDistribution
inverseF in interface DistributioninverseF in class ContinuousDistributionu - value at which the inverse distribution function is evaluated
public double getMean()
ContinuousDistribution
getMean in interface DistributiongetMean in class ContinuousDistributionpublic double getVariance()
ContinuousDistribution
getVariance in interface DistributiongetVariance in class ContinuousDistributionpublic double getStandardDeviation()
ContinuousDistribution
getStandardDeviation in interface DistributiongetStandardDeviation in class ContinuousDistribution
public static double density(double alpha,
double beta,
double x)
public static double cdf(double alpha,
double beta,
double x)
public static double barF(double alpha,
double beta,
double x)
public static double inverseF(double alpha,
double beta,
double u)
public static double[] getMLE(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 CauchyDist getInstanceFromMLE(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(double alpha,
double beta)
UnsupportedOperationException - the mean of the Cauchy distribution is undefined.
public static double getVariance(double alpha,
double beta)
public static double getStandardDeviation(double alpha,
double beta)
public double getAlpha()
public double getBeta()
public void setParams(double alpha,
double beta)
public double[] getParams()
public String toString()
toString in class Object
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