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SSJ V. 2.6. |
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java.lang.Object umontreal.iro.lecuyer.probdist.ContinuousDistribution umontreal.iro.lecuyer.probdist.TriangularDist
public class TriangularDist
Extends the class ContinuousDistribution
for
the triangular distribution with domain [a, b] and mode
(or shape parameter) m, where
a <= m <= b.
The density function is
f (x) = | 2(x - a)/[(b - a)(m - a)] | for a <= x <= m, |
f (x) = | 2(b - x)/[(b - a)(b - m)] | for m <= x <= b, |
f (x) = | 0 | elsewhere, |
F(x) = | 0 | for x < a, |
F(x) = | (x - a)2/[(b - a)(m - a)] | if a <= x <= m, |
F(x) = | 1 - (b - x)2/[(b - a)(b - m)] | if m <= x <= b, |
F(x) = | 1 | for x > b, |
F-1(u) = | a + ((b - a)(m - a)u)1/2 | if 0 <= u <= (m - a)/(b - a), |
F-1(u) = | b - ((b - a)(b - m)(1 - u))1/2 | if (m - a)/(b - a <= u <= 1. |
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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TriangularDist()
Constructs a TriangularDist object with default parameters a = 0, b = 1, and m = 0.5. |
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TriangularDist(double m)
Constructs a TriangularDist object with parameters a = 0 , b = 1 and m = m. |
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TriangularDist(double a,
double b,
double m)
Constructs a TriangularDist object with parameters a, b and m. |
Method Summary | |
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double |
barF(double x)
Returns the complementary distribution function. |
static double |
barF(double a,
double b,
double m,
double x)
Computes the complementary distribution function. |
double |
cdf(double x)
Returns the distribution function F(x). |
static double |
cdf(double a,
double b,
double m,
double x)
Computes the distribution function. |
double |
density(double x)
Returns f (x), the density evaluated at x. |
static double |
density(double a,
double b,
double m,
double x)
Computes the density function. |
double |
getA()
Returns the value of a for this object. |
double |
getB()
Returns the value of b for this object. |
static TriangularDist |
getInstanceFromMLE(double[] x,
int n,
double a,
double b)
Creates a new instance of a triangular distribution with parameters a and b. |
double |
getM()
Returns the value of m for this object. |
double |
getMean()
Returns the mean. |
static double |
getMean(double a,
double b,
double m)
Computes and returns the mean E[X] = (a + b + m)/3 of the triangular distribution with parameters a, b, m. |
static double[] |
getMLE(double[] x,
int n,
double a,
double b)
Estimates the parameter m of the triangular distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. |
double[] |
getParams()
Return a table containing the parameters of the current distribution. |
double |
getStandardDeviation()
Returns the standard deviation. |
static double |
getStandardDeviation(double a,
double b,
double m)
Computes and returns the standard deviation of the triangular distribution with parameters a, b, m. |
double |
getVariance()
Returns the variance. |
static double |
getVariance(double a,
double b,
double m)
Computes and returns the variance Var[X] = (a2 + b2 + m2 - ab - am - bm)/18 of the triangular distribution with parameters a, b, m. |
double |
inverseF(double u)
Returns the inverse distribution function x = F-1(u). |
static double |
inverseF(double a,
double b,
double m,
double u)
Computes the inverse distribution function. |
void |
setParams(double a,
double b,
double m)
Sets the value of the parameters a, b and m for this object. |
String |
toString()
Returns a String containing information about the current distribution. |
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 TriangularDist()
public TriangularDist(double m)
public TriangularDist(double a, double b, double m)
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 a, double b, double m, double x)
public static double cdf(double a, double b, double m, double x)
public static double barF(double a, double b, double m, double x)
public static double inverseF(double a, double b, double m, double u)
public static double[] getMLE(double[] x, int n, double a, double b)
x
- the list of observations used to evaluate parametersn
- the number of observations used to evaluate parametersa
- lower limit of rangeb
- upper limit of range
public static TriangularDist getInstanceFromMLE(double[] x, int n, double a, double b)
x
- the list of observations used to evaluate parametersn
- the number of observations used to evaluate parametersa
- lower limit of rangeb
- upper limit of rangepublic static double getMean(double a, double b, double m)
public static double getVariance(double a, double b, double m)
public static double getStandardDeviation(double a, double b, double m)
public double getA()
public double getB()
public double getM()
public void setParams(double a, double b, double m)
public double[] getParams()
public String toString()
toString
in class Object
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