|
SSJ V. 1.2.5. |
||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |
java.lang.Objectumontreal.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 |
---|
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
---|
decPrec |
Constructor Summary | |
---|---|
BetaDist(double alpha,
double beta)
Constructs a BetaDist object with parameters α = alpha and β = beta and default domain (0, 1). |
|
BetaDist(double alpha,
double beta,
double a,
double b)
Constructs a BetaDist object with parameters α = alpha and β = beta, and domain (a, b). |
|
BetaDist(double alpha,
double beta,
double a,
double b,
int d)
Constructs a BetaDist object with parameters α = alpha and β = beta, and approximations of roughly d decimal digits of precision when computing distribution, complementary distribution, and inverse functions. |
|
BetaDist(double alpha,
double beta,
int d)
Constructs a BetaDist object with parameters α = alpha and β = beta, and approximations of roughly d decimal digits of precision when computing the distribution, complementary distribution, and inverse functions. |
Method Summary | |
---|---|
static double |
barF(double alpha,
double beta,
double a,
double b,
int d,
double x)
Computes the complementary distribution function. |
static double |
barF(double alpha,
double beta,
int d,
double x)
Same as barF (alpha, beta, 0, 1, d, x). |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(double alpha,
double beta,
double a,
double b,
int d,
double x)
Computes an approximation of the distribution function, with roughly d decimal digits of precision. |
static double |
cdf(double alpha,
double beta,
int d,
double x)
Same as cdf (alpha, beta, 0, 1, d, x). |
double |
density(double x)
Returns f (x), the density of X 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 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 beta distribution over the interval [0, 1] 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] = α/(α + β) of the beta distribution with parameters α and β. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double alpha,
double beta)
Computes the standard deviation of the beta distribution with parameters α and β. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double alpha,
double beta)
. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
static double |
inverseF(double alpha,
double beta,
double a,
double b,
int d,
double u)
Returns the inverse beta distribution function using the algorithm implemented in the Cephes math library. |
static double |
inverseF(double alpha,
double beta,
int d,
double u)
Same as inverseF (alpha, beta, 0, 1, d, u). |
void |
setParams(double alpha,
double beta,
double a,
double b,
int d)
|
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
---|
barF, inverseBisection, inverseBrent |
Methods inherited from class java.lang.Object |
---|
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
---|
public BetaDist(double alpha, double beta)
public BetaDist(double alpha, double beta, double a, double b)
public BetaDist(double alpha, double beta, int d)
public BetaDist(double alpha, double beta, double a, double b, int d)
Method Detail |
---|
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 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)
density
(alpha, beta, 0, 1, x).
public static double density(double alpha, double beta, double a, double b, double x)
public static double cdf(double alpha, double beta, int d, double x)
cdf
(alpha, beta, 0, 1, d, x).
public static double cdf(double alpha, double beta, double a, double b, int d, double x)
public static double barF(double alpha, double beta, int d, double x)
barF
(alpha, beta, 0, 1, d, x).
public static double barF(double alpha, double beta, double a, double b, int d, double x)
public static double inverseF(double alpha, double beta, int d, double u)
inverseF
(alpha, beta, 0, 1, d, u).
public static double inverseF(double alpha, double beta, double a, double b, int d, double u)
cdf
method. The argument d gives
a good idea of the precision attained.
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, 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 double getA()
public double getB()
public void setParams(double alpha, double beta, double a, double b, int d)
|
SSJ V. 1.2.5. |
||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |