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java.lang.Object umontreal.iro.lecuyer.probdist.ContinuousDistribution umontreal.iro.lecuyer.probdist.RayleighDist
public class RayleighDist
This class extends the class ContinuousDistribution
for
the Rayleigh distribution with
location parameter a, and scale parameter β > 0.
The density 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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RayleighDist(double beta)
Constructs a RayleighDist object with parameters a = 0 and β = beta. |
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RayleighDist(double a,
double beta)
Constructs a RayleighDist object with parameters a = a, and β = beta. |
Method Summary | |
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double |
barF(double x)
Returns the complementary distribution function. |
static double |
barF(double beta,
double x)
Same as barF (0, beta, x). |
static double |
barF(double a,
double beta,
double x)
Computes the complementary distribution function. |
double |
cdf(double x)
Returns the distribution function F(x). |
static double |
cdf(double beta,
double x)
Same as cdf (0, beta, x). |
static double |
cdf(double a,
double beta,
double x)
Computes the distribution function. |
double |
density(double x)
Returns f (x), the density evaluated at x. |
static double |
density(double beta,
double x)
Same as density (0, beta, x). |
static double |
density(double a,
double beta,
double x)
Computes the density function. |
double |
getA()
Returns the parameter a. |
static RayleighDist |
getInstanceFromMLE(double[] x,
int n,
double a)
Creates a new instance of a Rayleigh distribution with parameters a and hat(β). |
double |
getMean()
Returns the mean. |
static double |
getMean(double a,
double beta)
Returns the mean a + β(π/2)1/2 of the Rayleigh distribution with parameters a and β. |
static double[] |
getMLE(double[] x,
int n,
double a)
Estimates the parameter β of the Rayleigh distribution using the maximum likelihood method, assuming that a is known, from the n observations x[i], i = 0, 1,…, n - 1. |
double[] |
getParams()
Return an array containing the parameters of the current distribution in the order: [a, β]. |
double |
getSigma()
Returns the parameter β. |
double |
getStandardDeviation()
Returns the standard deviation. |
static double |
getStandardDeviation(double beta)
Returns the standard deviation β(2 - π/2)1/2 of the Rayleigh distribution with parameter β. |
double |
getVariance()
Returns the variance. |
static double |
getVariance(double beta)
Returns the variance of the Rayleigh distribution with parameter β. |
double |
inverseF(double u)
Returns the inverse distribution function x = F-1(u). |
static double |
inverseF(double beta,
double u)
Same as inverseF (0, beta, u). |
static double |
inverseF(double a,
double beta,
double u)
Computes the inverse of the distribution function. |
void |
setParams(double a,
double beta)
Sets the parameters a and β for this object. |
String |
toString()
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Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, wait, wait, wait |
Constructor Detail |
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public RayleighDist(double beta)
public RayleighDist(double a, 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)
ContinuousDistribution
barF
in interface Distribution
barF
in class ContinuousDistribution
x
- value at which the complementary distribution function is evaluated
public double inverseF(double u)
ContinuousDistribution
inverseF
in interface Distribution
inverseF
in class ContinuousDistribution
u
- value at which the inverse distribution function is evaluated
public double getMean()
ContinuousDistribution
getMean
in interface Distribution
getMean
in class ContinuousDistribution
public double getVariance()
ContinuousDistribution
getVariance
in interface Distribution
getVariance
in class ContinuousDistribution
public double getStandardDeviation()
ContinuousDistribution
getStandardDeviation
in interface Distribution
getStandardDeviation
in class ContinuousDistribution
public static double density(double a, double beta, double x)
a
- the location parameterbeta
- the scale parameterx
- the value at which the density is evaluated
public static double density(double beta, double x)
beta
- the scale parameterx
- the value at which the density is evaluated
public static double cdf(double a, double beta, double x)
a
- the location parameterbeta
- the scale parameterx
- the value at which the distribution is evaluated
public static double cdf(double beta, double x)
beta
- the scale parameterx
- the value at which the distribution is evaluated
public static double barF(double a, double beta, double x)
a
- the location parameterbeta
- the scale parameterx
- the value at which the complementary distribution is evaluated
public static double barF(double beta, double x)
beta
- the scale parameterx
- the value at which the complementary distribution is evaluated
public static double inverseF(double a, double beta, double u)
a
- the location parameterbeta
- the scale parameteru
- the value at which the inverse distribution is evaluated
public static double inverseF(double beta, double u)
beta
- the scale parameteru
- the value at which the inverse distribution is evaluated
public static double[] getMLE(double[] x, int n, double a)
x
- the list of observations to use to evaluate parametersn
- the number of observations to use to evaluate parametersa
- the location parameter
public static RayleighDist getInstanceFromMLE(double[] x, int n, double a)
x
- the list of observations to use to evaluate parametersn
- the number of observations to use to evaluate parametersa
- the location parameterpublic static double getMean(double a, double beta)
a
- the location parameterbeta
- the scale parameter
public static double getVariance(double beta)
beta
- the scale parameter
public static double getStandardDeviation(double beta)
beta
- the scale parameter
public double getA()
public double getSigma()
public void setParams(double a, double beta)
a
- the location parameterbeta
- the scale parameterpublic double[] getParams()
public String toString()
toString
in class Object
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