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java.lang.Object umontreal.iro.lecuyer.probdist.ContinuousDistribution umontreal.iro.lecuyer.probdist.BetaDist
public class BetaDist
Extends the class ContinuousDistribution
for
the beta distribution with shape parameters
α > 0 and β > 0, over the interval [a, b], where a < b.
It has density
GammaDist
.
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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BetaDist(double alpha,
double beta)
Constructs a BetaDist object with parameters α = alpha, β = beta and default domain [0, 1]. |
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BetaDist(double alpha,
double beta,
double a,
double b)
Constructs a BetaDist object with parameters α = alpha, β = beta and domain [a, b]. |
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BetaDist(double alpha,
double beta,
double a,
double b,
int d)
Deprecated. |
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BetaDist(double alpha,
double beta,
int d)
Deprecated. |
Method Summary | |
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double |
barF(double x)
Returns the complementary distribution function. |
static double |
barF(double alpha,
double beta,
double x)
Same as barF (alpha, beta, 0, 1, x). |
static double |
barF(double alpha,
double beta,
double a,
double b,
double x)
Computes the complementary distribution function. |
static double |
barF(double alpha,
double beta,
double a,
double b,
int d,
double x)
Deprecated. |
static double |
barF(double alpha,
double beta,
int d,
double x)
Deprecated. |
double |
cdf(double x)
Returns the distribution function F(x). |
static double |
cdf(double alpha,
double beta,
double x)
Same as cdf (alpha, beta, 0, 1, x). |
static double |
cdf(double alpha,
double beta,
double a,
double b,
double x)
Computes the distribution function. |
static double |
cdf(double alpha,
double beta,
double a,
double b,
int d,
double x)
Deprecated. |
static double |
cdf(double alpha,
double beta,
int d,
double x)
Deprecated. |
double |
density(double x)
Returns f (x), the density evaluated at x. |
static double |
density(double alpha,
double beta,
double x)
Same as density (alpha, beta, 0, 1, x). |
static double |
density(double alpha,
double beta,
double a,
double b,
double x)
Computes the density function of the beta distribution. |
double |
getA()
Returns the parameter a of this object. |
double |
getAlpha()
Returns the parameter α of this object. |
double |
getB()
Returns the parameter b of this object. |
double |
getBeta()
Returns the parameter β of this object. |
static BetaDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a beta distribution with parameters α and β over the interval [0, 1] 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 alpha,
double beta)
Computes and returns the mean E[X] = α/(α + β) of the beta distribution with parameters α and β, over the interval [0, 1]. |
static double |
getMean(double alpha,
double beta,
double a,
double b)
Computes and returns the mean E[X] = (bα + aβ)/(α + β) of the beta distribution with parameters α and β over the interval [a, b]. |
static double[] |
getMLE(double[] x,
int n)
Estimates the parameters (α, β) of the beta distribution over the interval [0, 1] using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. |
double[] |
getParams()
Return an array containing the parameters of the current distribution as [α, β, a, b]. |
double |
getStandardDeviation()
Returns the standard deviation. |
static double |
getStandardDeviation(double alpha,
double beta)
Computes the standard deviation of the beta distribution with parameters α and β, over the interval [0, 1]. |
static double |
getStandardDeviation(double alpha,
double beta,
double a,
double b)
Computes the standard deviation of the beta distribution with parameters α and β, over the interval [a, b]. |
double |
getVariance()
Returns the variance. |
static double |
getVariance(double alpha,
double beta)
Computes and returns the variance Var[X] = 1#1 of the beta distribution with parameters α and β, over the interval [0, 1]. |
static double |
getVariance(double alpha,
double beta,
double a,
double b)
Computes and returns the variance Var[X] = 2#2 of the beta distribution with parameters α and β, over the interval [a, b]. |
double |
inverseF(double u)
Returns the inverse distribution function x = F-1(u). |
static double |
inverseF(double alpha,
double beta,
double u)
Same as inverseF (alpha, beta, 0, 1, u). |
static double |
inverseF(double alpha,
double beta,
double a,
double b,
double u)
Returns the inverse beta distribution function using the algorithm implemented in the Cephes math library. |
static double |
inverseF(double alpha,
double beta,
double a,
double b,
int d,
double u)
Deprecated. |
static double |
inverseF(double alpha,
double beta,
int d,
double u)
Deprecated. |
void |
setParams(double alpha,
double beta,
double a,
double b)
Sets the parameters of the current distribution. |
void |
setParams(double alpha,
double beta,
double a,
double b,
int d)
Deprecated. |
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 BetaDist(double alpha, double beta)
public BetaDist(double alpha, double beta, double a, double b)
@Deprecated public BetaDist(double alpha, double beta, int d)
@Deprecated public BetaDist(double alpha, double beta, double a, double b, int d)
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 alpha, double beta, double x)
density
(alpha, beta, 0, 1, x).
public static double density(double alpha, double beta, double a, double b, double x)
@Deprecated public static double cdf(double alpha, double beta, int d, double x)
@Deprecated public static double cdf(double alpha, double beta, double a, double b, int d, double x)
@Deprecated public static double barF(double alpha, double beta, int d, double x)
@Deprecated public static double barF(double alpha, double beta, double a, double b, int d, double x)
public static double cdf(double alpha, double beta, double x)
cdf
(alpha, beta, 0, 1, x).
public static double cdf(double alpha, double beta, double a, double b, double x)
public static double barF(double alpha, double beta, double x)
barF
(alpha, beta, 0, 1, x).
public static double barF(double alpha, double beta, double a, double b, double x)
@Deprecated public static double inverseF(double alpha, double beta, int d, double u)
public static double inverseF(double alpha, double beta, double u)
inverseF
(alpha, beta, 0, 1, u).
@Deprecated public static double inverseF(double alpha, double beta, double a, double b, int d, double u)
public static double inverseF(double alpha, double beta, double a, double b, 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 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 getMean(double alpha, double beta)
public static double getMean(double alpha, double beta, double a, double b)
public static double getVariance(double alpha, double beta)
public static double getVariance(double alpha, double beta, double a, double b)
public static double getStandardDeviation(double alpha, double beta)
public static double getStandardDeviation(double alpha, double beta, double a, double b)
public double getAlpha()
public double getBeta()
public double getA()
public double getB()
@Deprecated public void setParams(double alpha, double beta, double a, double b, int d)
public void setParams(double alpha, double beta, double a, double b)
public double[] getParams()
public String toString()
toString
in class Object
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SSJ V. 2.6. |
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SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |