SSJ  3.3.1
Stochastic Simulation in Java
Public Member Functions | Static Public Member Functions | List of all members
LognormalDist Class Reference

Extends the class ContinuousDistribution for the lognormal distribution [99] . More...

Inheritance diagram for LognormalDist:
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Collaboration diagram for LognormalDist:
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Public Member Functions

 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)
 
double cdf (double x)
 Returns the distribution function \(F(x)\). More...
 
double barF (double x)
 Returns \(\bar{F}(x) = 1 - F(x)\). More...
 
double inverseF (double u)
 Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More...
 
double getMean ()
 Returns the mean of the distribution function.
 
double getVariance ()
 Returns the variance of the distribution function.
 
double getStandardDeviation ()
 Returns the standard deviation of the distribution function.
 
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 ContinuousDistribution
abstract double density (double x)
 Returns \(f(x)\), the density evaluated at \(x\). More...
 
double barF (double x)
 Returns the complementary distribution function. More...
 
double inverseBrent (double a, double b, double u, double tol)
 Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method. More...
 
double inverseBisection (double u)
 Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection. More...
 
double inverseF (double u)
 Returns the inverse distribution function \(x = F^{-1}(u)\). More...
 
double getMean ()
 Returns the mean. More...
 
double getVariance ()
 Returns the variance. More...
 
double getStandardDeviation ()
 Returns the standard deviation. More...
 
double getXinf ()
 Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
double getXsup ()
 Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
void setXinf (double xa)
 Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
void setXsup (double xb)
 Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 

Static Public Member Functions

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 \(\bar{F}(x)\), using NormalDist.barF01.
 
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 \(x[i]\), \(i = 0, 1,…, n-1\). More...
 
static LognormalDist getInstanceFromMLE (double[] x, int n)
 Creates a new instance of a lognormal distribution with parameters \(\mu\) and \(\sigma\) estimated using the maximum likelihood method based on the \(n\) observations \(x[i]\), \(i = 0, 1, …, n-1\). More...
 
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 \(\sigma\). More...
 
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 \(\sigma\). More...
 
static double getStandardDeviation (double mu, double sigma)
 Computes and returns the standard deviation of the lognormal distribution with parameters \(\mu\) and \(\sigma\). More...
 

Additional Inherited Members

- Public Attributes inherited from ContinuousDistribution
int decPrec = 15
 
- Protected Attributes inherited from ContinuousDistribution
double supportA = Double.NEGATIVE_INFINITY
 
double supportB = Double.POSITIVE_INFINITY
 
- Static Protected Attributes inherited from ContinuousDistribution
static final double XBIG = 100.0
 
static final double XBIGM = 1000.0
 
static final double [] EPSARRAY
 

Detailed Description

Extends the class ContinuousDistribution for the lognormal distribution [99] .

(See also the Johnson \(S_L\) distribution JohnsonSLDist in this package.) It has scale parameter \(\mu\) and shape parameter \(\sigma> 0\). The density is

\[ f(x) = \frac{1}{\sqrt{2\pi}\sigma x} e^{-(\ln(x) - \mu)^2/(2\sigma^2)} \qquad\mbox{for } x>0, \tag{flognormal} \]

and 0 elsewhere. The distribution function is

\[ F(x) = \Phi\left({(\ln(x) - \mu)/\sigma}\right) \qquad\mbox{for } x>0, \]

where \(\Phi\) is the standard normal distribution function. Its inverse is given by

\[ F^{-1}(u) = e^{\mu+ \sigma\Phi^{-1} (u)} \qquad\mbox{for } 0 \le u < 1. \]

If \(\ln(Y)\) has a normal distribution, then \(Y\) has a lognormal distribution with the same parameters.

This class relies on the methods NormalDist.cdf01 and NormalDist.inverseF01 of NormalDist to approximate \(\Phi\) and \(\Phi^{-1}\).

Member Function Documentation

◆ barF()

double barF ( double  x)

Returns \(\bar{F}(x) = 1 - F(x)\).

Parameters
xvalue at which the complementary distribution function is evaluated
Returns
complementary distribution function evaluated at x

Implements Distribution.

◆ cdf()

double cdf ( double  x)

Returns the distribution function \(F(x)\).

Parameters
xvalue at which the distribution function is evaluated
Returns
distribution function evaluated at x

Implements Distribution.

◆ getInstanceFromMLE()

static LognormalDist getInstanceFromMLE ( double []  x,
int  n 
)
static

Creates a new instance of a lognormal distribution with parameters \(\mu\) and \(\sigma\) estimated using the maximum likelihood method based on the \(n\) observations \(x[i]\), \(i = 0, 1, …, n-1\).

Parameters
xthe list of observations to use to evaluate parameters
nthe number of observations to use to evaluate parameters

◆ getMean()

static double getMean ( double  mu,
double  sigma 
)
static

Computes and returns the mean \(E[X] = e^{\mu+ \sigma^2/2}\) of the lognormal distribution with parameters \(\mu\) and \(\sigma\).

Returns
the mean of the lognormal distribution

◆ getMLE()

static double [] getMLE ( double []  x,
int  n 
)
static

Estimates the parameters \((\mu, \sigma)\) of the lognormal distribution using the maximum likelihood method, from the \(n\) observations \(x[i]\), \(i = 0, 1,…, n-1\).

The estimates are returned in a two-element array, in regular order: [ \(\mu\), \(\sigma\)]. The maximum likelihood estimators are the values \((\hat{\mu}, \hat{\sigma})\) that satisfy the equations:

\begin{align*} \hat{\mu} & = \frac{1}{n} \sum_{i=1}^n \ln(x_i) \\ \hat{\sigma} & = \sqrt{\frac{1}{n} \sum_{i=1}^n (\ln(x_i) - \hat{\mu})^2}. \end{align*}

See [99]  (page 220).

Parameters
xthe list of observations used to evaluate parameters
nthe number of observations used to evaluate parameters
Returns
returns the parameters [ \(\hat{\mu}\), \(\hat{\sigma}\)]

◆ getStandardDeviation()

static double getStandardDeviation ( double  mu,
double  sigma 
)
static

Computes and returns the standard deviation of the lognormal distribution with parameters \(\mu\) and \(\sigma\).

Returns
the standard deviation of the lognormal distribution

◆ getVariance()

static double getVariance ( double  mu,
double  sigma 
)
static

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 \(\sigma\).

Returns
the variance of the lognormal distribution

◆ inverseF()

double inverseF ( double  u)

Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).

Parameters
uvalue in the interval \((0,1)\) for which the inverse distribution function is evaluated
Returns
the inverse distribution function evaluated at u

Implements Distribution.


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