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SSJ V. 2.6.2. |
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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.Pearson6Dist
public class Pearson6Dist
Extends the class ContinuousDistribution for
the Pearson type VI distribution with shape parameters
α1 > 0 and
α2 > 0, 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 | |
|---|---|
Pearson6Dist(double alpha1,
double alpha2,
double beta)
Constructs a Pearson6Dist object with parameters α1 = alpha1, α2 = alpha2 and β = beta. |
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| Method Summary | |
|---|---|
double |
barF(double x)
Returns the complementary distribution function. |
static double |
barF(double alpha1,
double alpha2,
double beta,
double x)
Computes the complementary distribution function of a Pearson VI distribution with shape parameters α1 and α2, and scale parameter β. |
double |
cdf(double x)
Returns the distribution function F(x). |
static double |
cdf(double alpha1,
double alpha2,
double beta,
double x)
Computes the distribution function of a Pearson VI distribution with shape parameters α1 and α2, and scale parameter β. |
double |
density(double x)
Returns f (x), the density evaluated at x. |
static double |
density(double alpha1,
double alpha2,
double beta,
double x)
Computes the density function of a Pearson VI distribution with shape parameters α1 and α2, and scale parameter β. |
double |
getAlpha1()
Returns the α1 parameter of this object. |
double |
getAlpha2()
Returns the α2 parameter of this object. |
double |
getBeta()
Returns the β parameter of this object. |
static Pearson6Dist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a Pearson VI distribution with parameters α1, α2 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 alpha1,
double alpha2,
double beta)
Computes and returns the mean E[X] = (βα1)/(α2 - 1) of a Pearson VI distribution with shape parameters α1 and α2, and scale parameter β. |
static double[] |
getMLE(double[] x,
int n)
Estimates the parameters (α1, α2, β) of the Pearson VI distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. |
double[] |
getParams()
Return a table containing the parameters of the current distribution. |
double |
getStandardDeviation()
Returns the standard deviation. |
static double |
getStandardDeviation(double alpha1,
double alpha2,
double beta)
Computes and returns the standard deviation of a Pearson VI distribution with shape parameters α1 and α2, and scale parameter β. |
double |
getVariance()
Returns the variance. |
static double |
getVariance(double alpha1,
double alpha2,
double beta)
Computes and returns the variance Var[X] = [β2α1(α1 + α2 -1)]/[(α2 -1)2(α2 - 2)] of a Pearson VI distribution with shape parameters α1 and α2, and scale parameter β. |
double |
inverseF(double u)
Returns the inverse distribution function x = F-1(u). |
static double |
inverseF(double alpha1,
double alpha2,
double beta,
double u)
Computes the inverse distribution function of a Pearson VI distribution with shape parameters α1 and α2, and scale parameter β. |
void |
setParam(double alpha1,
double alpha2,
double beta)
Sets the parameters α1, α2 and β of 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 Pearson6Dist(double alpha1,
double alpha2,
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 alpha1,
double alpha2,
double beta,
double x)
public static double cdf(double alpha1,
double alpha2,
double beta,
double x)
public static double barF(double alpha1,
double alpha2,
double beta,
double x)
public static double inverseF(double alpha1,
double alpha2,
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 Pearson6Dist 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 alpha1,
double alpha2,
double beta)
public static double getVariance(double alpha1,
double alpha2,
double beta)
public static double getStandardDeviation(double alpha1,
double alpha2,
double beta)
public double getAlpha1()
public double getAlpha2()
public double getBeta()
public void setParam(double alpha1,
double alpha2,
double beta)
public double[] getParams()
public String toString()
toString in class Object
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SSJ V. 2.6.2. |
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| PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD | ||||||||