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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.ExponentialDist
public class ExponentialDist
Extends the class ContinuousDistribution
for
the exponential distribution
with mean 1/λ where
λ > 0.
Its density is
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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ExponentialDist()
Constructs an ExponentialDist object with parameter λ = 1. |
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ExponentialDist(double lambda)
Constructs an ExponentialDist object with parameter λ = lambda. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
static double |
barF(double lambda,
double x)
Computes the complementary distribution function. |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(double lambda,
double x)
Computes the distribution function. |
double |
density(double x)
Returns f (x), the density of X evaluated at x. |
static double |
density(double lambda,
double x)
Computes the density function. |
static ExponentialDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of an exponential distribution with parameter λ estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
double |
getLambda()
Returns the value of λ for this object. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int n)
Estimates and returns the parameter [ hat(λ)] of the exponential distribution 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 lambda)
Computes and returns the mean, E[X] = 1/λ, of the exponential distribution with parameter λ. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double lambda)
Computes and returns the standard deviation of the exponential distribution with parameter λ. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double lambda)
Computes and returns the variance, Var[X] = 1/λ2, of the exponential distribution with parameter λ. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
static double |
inverseF(double lambda,
double u)
Computes the inverse distribution function. |
void |
setLambda(double lambda)
Sets the value of λ 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 ExponentialDist()
public ExponentialDist(double lambda)
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 lambda, double x)
public static double cdf(double lambda, double x)
public static double barF(double lambda, double x)
public static double inverseF(double lambda, double u)
public static ExponentialDist 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 used to evaluate parametersn
- the number of observations used to evaluate parameters
public static double getMean(double lambda)
public static double getVariance(double lambda)
public static double getStandardDeviation(double lambda)
public double getLambda()
public void setLambda(double lambda)
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