umontreal.ssj.probdist.LognormalDistFromMoments Class Reference

Extends the LognormalDist class with a constructor accepting the mean \(m\) and the variance \(v\) of the distribution as arguments. More...

Inheritance diagram for umontreal.ssj.probdist.LognormalDistFromMoments:

Additional Inherited Members
Public Member Functions inherited from umontreal.ssj.probdist.LognormalDist
	LognormalDist ()
	Constructs a LognormalDist object with default parameters \(\mu= 0\) and \(\sigma= 1\).
	LognormalDist (double mu, double sigma)
	Constructs a LognormalDist object with parameters \(\mu\) = mu and \(\sigma\) = sigma.
double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\).
double	cdf (double x)
	Returns the distribution function \(F(x)\).
double	barF (double x)
	Returns the complementary distribution function.
double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
double	getMean ()
	Returns the mean.
double	getVariance ()
	Returns the variance.
double	getStandardDeviation ()
	Returns the standard deviation.
double	getMu ()
	Returns the parameter \(\mu\) of this object.
double	getSigma ()
	Returns the parameter \(\sigma\) of this object.
void	setParams (double mu, double sigma)
	Sets the parameters \(\mu\) and \(\sigma\) of this object.
double[]	getParams ()
	Returns a table containing the parameters of the current distribution, in the order: [ \(\mu\), \(\sigma\)].
String	toString ()
	Returns a String containing information about the current distribution.
Public Member Functions inherited from umontreal.ssj.probdist.ContinuousDistribution
double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method.
double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection.
double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXinf (double xa)
	Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXsup (double xb)
	Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
Static Public Member Functions inherited from umontreal.ssj.probdist.LognormalDist
static double	density (double mu, double sigma, double x)
	Computes the lognormal density function \(f(x)\) in ( flognormal ).
static double	cdf (double mu, double sigma, double x)
	Computes the lognormal distribution function, using NormalDist.cdf01.
static double	barF (double mu, double sigma, double x)
	Computes the lognormal complementary distribution function.
static double	inverseF (double mu, double sigma, double u)
	Computes the inverse of the lognormal distribution function, using NormalDist.inverseF01.
static double[]	getMLE (double[] x, int n)
	Estimates the parameters \((\mu, \sigma)\) of the lognormal distribution using the maximum likelihood method, from the \(n\) observations \(x[i]\), \(i = 0, 1,…, n-1\).
static LognormalDist	getInstanceFromMLE (double[] x, int n)
	Creates a new instance of a lognormal distribution with parameters.
static double	getMean (double mu, double sigma)
	Computes and returns the mean \(E[X] = e^{\mu+ \sigma^2/2}\) of the lognormal distribution with parameters \(\mu\) and.
static double	getVariance (double mu, double sigma)
	Computes and returns the variance \(\mbox{Var}[X] = e^{2\mu+ \sigma^2}(e^{\sigma^2} - 1)\) of the lognormal distribution with parameters \(\mu\) and \(\sigma\).
static double	getStandardDeviation (double mu, double sigma)
	Computes and returns the standard deviation of the lognormal distribution with parameters \(\mu\) and \(\sigma\).

Detailed Description

Extends the LognormalDist class with a constructor accepting the mean \(m\) and the variance \(v\) of the distribution as arguments.

The mean and variance of a lognormal random variable with parameters

\(\mu\) and \(\sigma\) are \(e^{\mu+\sigma^2/2}\) and \(e^{2\mu+ \sigma^2}(e^{\sigma^2} - 1)\) respectively, so the parameters are given by \(\sigma=\sqrt{\ln(v/m^2+1)}\) and \(\mu=\ln(m) - \sigma^2/2\).

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Definition at line 42 of file LognormalDistFromMoments.java.

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The documentation for this class was generated from the following file:

• src/main/java/umontreal/ssj/probdist/LognormalDistFromMoments.java