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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 |
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Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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decPrec |
Constructor Summary | |
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Pearson6Dist(double alpha1,
double alpha2,
double beta)
Constructs a Pearson6Dist object with parameters α1 = alpha1, α2 = alpha2 and β = beta. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
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)
Computes and 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 of X 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 in table x[i], i = 0, 1,…, n - 1. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int n)
Estimates and returns the parameters [ hat(α_1), hat(α_2), hat(β)] of the Pearson VI 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 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. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
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 of the distribution function. |
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)
Computes and returns the inverse distribution function F-1(u), defined in. |
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. |
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 Pearson6Dist(double alpha1, double alpha2, 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 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 Pearson6Dist 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 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)
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SSJ V. 1.2.5. |
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PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |