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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.PiecewiseLinearEmpiricalDist
public class PiecewiseLinearEmpiricalDist
Extends the class ContinuousDistribution
for a piecewise-linear
approximation of the empirical distribution function,
based on the observations
X(1),..., X(n) (sorted by increasing order),
and defined as follows (e.g.,).
The distribution function starts at X(1) and climbs linearly by 1/(n - 1)
between any two successive observations. The density is
F(x) = | 0 | for x < X(1), |
F(x) = | (i - 1)/(n - 1) + (x - X(i))/[(n - 1)(X(i+1) - X(i))] | for X(i) <= x < X(i+1), |
F(x) = | 1 | elsewhere, |
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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PiecewiseLinearEmpiricalDist(double[] obs)
Constructs a new piecewise-linear distribution using all the observations stored in obs. |
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PiecewiseLinearEmpiricalDist(Reader in)
Constructs a new empirical distribution using the observations read from the reader in. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
double |
density(double x)
Returns f (x), the density of X evaluated at x. |
double |
getMean()
Returns the mean of the distribution function. |
int |
getN()
Returns n, the number of observations. |
double |
getObs(int i)
Returns the value of X(i). |
double |
getSampleMean()
Returns the sample mean of the observations. |
double |
getSampleStandardDeviation()
Returns the sample standard deviation of the observations. |
double |
getSampleVariance()
Returns the sample variance of the observations. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
double |
getVariance()
Returns the variance of the distribution function. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
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 PiecewiseLinearEmpiricalDist(double[] obs)
public PiecewiseLinearEmpiricalDist(Reader in) throws IOException
IOException
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 int getN()
public double getObs(int i)
public double getSampleMean()
public double getSampleVariance()
public double getSampleStandardDeviation()
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SSJ V. 1.2.5. |
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