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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.BetaDist
umontreal.iro.lecuyer.probdist.BetaSymmetricalDist
public class BetaSymmetricalDist
Specializes the class BetaDist
to the case of a symmetrical
beta distribution over the interval [0, 1],
with shape parameters
α = β.
A faster inversion method is implemented here for this special case.
Because of the symmetry around 1/2, four series are used to compute the
cdf, two around x = 0 and two around x = 1/2.
Given u, one then solves each series for x by using the
Newton-Raphson method which shows quadratic convergence when the
starting iterate is close enough to the solution x.
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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BetaSymmetricalDist(double alpha)
Constructs a BetaSymmetricalDist object with parameters α = β = alpha, over the unit interval (0, 1). |
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BetaSymmetricalDist(double alpha,
int d)
Same as BetaSymmetricalDist (alpha), but using approximations of roughly d decimal digits of precision when computing the distribution, complementary distribution, and inverse functions. |
Method Summary | |
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static double |
barF(double alpha,
int d,
double x)
Same as barF (alpha, beta, d, x). |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(double alpha,
int d,
double x)
Same as cdf (alpha, alpha, d, x). |
static double |
density(double alpha,
double x)
Returns the density evaluated at x. |
static BetaDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a symmetrical beta distribution with parameter α 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 parameter [ hat(α)] of the symmetrical beta 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)
Computes and returns the mean E[X] = 1/2 of the symmetrical beta distribution with parameter α. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double alpha)
Computes and returns the standard deviation of the symmetrical beta distribution with parameter α. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double alpha)
Computes and returns the variance, Var[X] = 1/(8α + 4), of the symmetrical beta distribution with parameter α. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
static double |
inverseF(double alpha,
double u)
Returns the inverse distribution function evaluated at u, for the symmetrical beta distribution over the interval [0, 1], with shape parameters 0 < α = β = alpha. |
void |
setParams(double alpha,
double beta,
double a,
double b,
int d)
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Methods inherited from class umontreal.iro.lecuyer.probdist.BetaDist |
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barF, barF, cdf, cdf, density, density, density, getA, getAlpha, getB, getBeta, getMean, getStandardDeviation, getVariance, inverseF, inverseF |
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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barF, 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 BetaSymmetricalDist(double alpha)
public BetaSymmetricalDist(double alpha, int d)
Method Detail |
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public double cdf(double x)
Distribution
cdf
in interface Distribution
cdf
in class BetaDist
x
- value at which the distribution function is evaluated
public double inverseF(double u)
Distribution
inverseF
in interface Distribution
inverseF
in class BetaDist
u
- value in the interval (0, 1) for which the inverse
distribution function is evaluated
public static double density(double alpha, double x)
public static double cdf(double alpha, int d, double x)
cdf
(alpha, alpha, d, x).
public static double barF(double alpha, int d, double x)
barF
(alpha, beta, d, x).
public static double inverseF(double alpha, double u)
public double getMean()
Distribution
getMean
in interface Distribution
getMean
in class BetaDist
public double getVariance()
Distribution
getVariance
in interface Distribution
getVariance
in class BetaDist
public double getStandardDeviation()
Distribution
getStandardDeviation
in interface Distribution
getStandardDeviation
in class BetaDist
public static BetaDist 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)
public static double getVariance(double alpha)
public static double getStandardDeviation(double alpha)
public void setParams(double alpha, double beta, double a, double b, int d)
setParams
in class BetaDist
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