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SSJ V. 1.2.5. |
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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.Pearson5Dist
public class Pearson5Dist
Extends the class ContinuousDistribution
for
the Pearson type V distribution with shape parameter
α > 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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Pearson5Dist(double alpha,
double beta)
Constructs a Pearson5Dist 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 function of a Pearson V distribution with shape parameter α and scale parameter β. |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(double alpha,
double beta,
double x)
Computes the density function of a Pearson V distribution with shape parameter α and scale parameter β. |
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 of a Pearson V distribution with shape parameter α and scale parameter β. |
double |
getAlpha()
Returns the α parameter of this object. |
double |
getBeta()
Returns the β parameter of this object. |
static Pearson5Dist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a Pearson V 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 Pearson V 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)
Computes and returns the mean E[X] = β/(α - 1) of a Pearson V distribution with shape parameter α and scale parameter β. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double alpha,
double beta)
Computes and returns the standard deviation of a Pearson V distribution with shape parameter α and scale parameter β. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double alpha,
double beta)
Computes and returns the variance Var[X] = β2/((α -1)2(α - 2) of a Pearson V distribution with shape parameter α and scale parameter β. |
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 distribution function of a Pearson V distribution with shape parameter α and scale parameter β. |
void |
setParam(double alpha,
double beta)
Sets the parameters α 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 Pearson5Dist(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 Pearson5Dist 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)
public static double getVariance(double alpha, double beta)
public static double getStandardDeviation(double alpha, double beta)
public double getAlpha()
public double getBeta()
public void setParam(double alpha, double beta)
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SSJ V. 1.2.5. |
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SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |