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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.LognormalDist
public class LognormalDist
Extends the class ContinuousDistribution
for the
lognormal distribution. It has scale
parameter μ and shape parameter
σ > 0.
The density is
This class relies on the methods
NormalDist.cdf01
and
NormalDist.inverseF01
of NormalDist
to approximate Φ and Φ-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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LognormalDist()
Constructs a LognormalDist object with default parameters μ = 0 and σ = 1. |
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LognormalDist(double mu,
double sigma)
Constructs a LognormalDist object with parameters μ = mu and σ = sigma. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
static double |
barF(double mu,
double sigma,
double x)
Computes the lognormal complementary distribution function bar(F)(x), using NormalDist.barF01 . |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(double mu,
double sigma,
double x)
Computes the lognormal distribution function, using cdf01 . |
double |
density(double x)
Returns f (x), the density of X evaluated at x. |
static double |
density(double mu,
double sigma,
double x)
Computes the lognormal density function f (x). |
static LognormalDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a lognormal distribution with parameters μ and σ 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(μ), hat(σ)] of the log-normal 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 mu,
double sigma)
Computes and returns the mean E[X] = eμ+σ2/2 of the lognormal distribution with parameters μ and σ. |
double |
getMu()
Returns the parameter μ of this object. |
double |
getSigma()
Returns the parameter σ of this object. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double mu,
double sigma)
Computes and returns the standard deviation of the lognormal distribution with parameters μ and σ. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double mu,
double sigma)
Computes and returns the variance Var[X] = e2μ+σ2(eσ2 - 1) of the lognormal distribution with parameters μ and σ. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
static double |
inverseF(double mu,
double sigma,
double u)
Computes the inverse of the lognormal distribution function, using NormalDist.inverseF01 . |
void |
setParams(double mu,
double sigma)
Sets the parameters μ and σ of 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 LognormalDist()
public LognormalDist(double mu, double sigma)
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 mu, double sigma, double x)
public static double cdf(double mu, double sigma, double x)
cdf01
.
public static double barF(double mu, double sigma, double x)
NormalDist.barF01
.
public static double inverseF(double mu, double sigma, double u)
NormalDist.inverseF01
.
public static LognormalDist 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 mu, double sigma)
public static double getVariance(double mu, double sigma)
public static double getStandardDeviation(double mu, double sigma)
public double getMu()
public double getSigma()
public void setParams(double mu, double sigma)
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SSJ V. 1.2.5. |
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