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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 |
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Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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decPrec |
Constructor Summary | |
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CauchyDist()
Constructs a CauchyDist object with parameters α = 0 and β = 1. |
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CauchyDist(double alpha,
double beta)
Constructs a CauchyDist object with parameters α = alpha and β = beta. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
static double |
barF(double alpha,
double beta,
double x)
Computes the complementary distribution. |
double |
cdf(double x)
Computes and 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 of X 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 in table x[i], i = 0, 1,…, n - 1. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int n)
Estimates and returns the parameters [ hat(α), hat(β)] of the Cauchy 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(double alpha,
double beta)
Throws an exception since the mean does not exist. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double alpha,
double beta)
Returns ∞ since the standard deviation does not exist. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double alpha,
double beta)
Returns ∞ since the variance does not exist. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
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. |
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 CauchyDist()
public CauchyDist(double alpha, double beta)
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(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 CauchyDist 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(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)
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