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java.lang.Objectumontreal.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 bar(F)(x) = 1 - F(x). |
static double |
barF(double a,
double b,
double m,
double x)
Computes the complementary distribution function. |
double |
cdf(double x)
Computes and 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 of X 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. |
double |
getM()
Returns the value of m for this object. |
double |
getMean()
Returns the mean of the distribution function. |
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. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
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 of the distribution function. |
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)
Computes and returns the inverse distribution function F-1(u), defined in. |
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. |
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 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)
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 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 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)
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SSJ V. 1.2.5. |
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SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |