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., [114] (page 318)). More...

Inheritance diagram for umontreal.ssj.probdist.PiecewiseLinearEmpiricalDist:

Public Member Functions
	PiecewiseLinearEmpiricalDist (double[] obs)
	Constructs a new piecewise-linear distribution using all the observations stored in obs.
	PiecewiseLinearEmpiricalDist (Reader in) throws IOException
	Constructs a new empirical distribution using the observations read from the reader in.
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.
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	getSampleVariance ()
	Returns the sample variance of the observations.
double	getSampleStandardDeviation ()
	Returns the sample standard deviation of the observations.
double[]	getParams ()
	Return a table containing parameters of the current distribution.
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 \([x_a, x_b]\).

Detailed Description

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., [114] (page 318)).

The distribution function starts at \(X_{(1)}\) and climbs linearly by

\(1/(n-1)\) between any two successive observations. The density is

\[ f(x) = \frac{1}{(n-1)(X_{(i+1)} - X_{(i)})} \mbox{ for }X_{(i)}\le x < X_{(i+1)}\mbox{ and } i=1,2,…,n-1. \]

The distribution function is

\[ F(x) = \left\{\begin{array}{ll} 0 & \mbox{ for } x < X_{(1)}, \\ \displaystyle\frac{i-1}{n-1} + \frac{x - X_{(i)}}{(n-1)(X_{(i+1)} - X_{(i)})} & \mbox{ for } X_{(i)} \le x < X_{(i+1)} \mbox{ and } i<n, \\ 1 & \mbox{ for } x \ge X_{(n)}, \end{array}\right. \]

whose inverse is

\[ F^{-1}(u) = X_{(i)} + ((n-1)u - i + 1)(X_{(i+1)} - X_{(i)}) \]

for \((i-1)/(n-1)\le u \le i/(n-1)\) and \(i=1,…,n-1\).

Definition at line 58 of file PiecewiseLinearEmpiricalDist.java.

Constructor & Destructor Documentation

◆ PiecewiseLinearEmpiricalDist() [1/2]

umontreal.ssj.probdist.PiecewiseLinearEmpiricalDist.PiecewiseLinearEmpiricalDist ( double[] obs )

Constructs a new piecewise-linear distribution using all the observations stored in obs.

These observations are copied into an internal array and then sorted.

Definition at line 71 of file PiecewiseLinearEmpiricalDist.java.

◆ PiecewiseLinearEmpiricalDist() [2/2]

umontreal.ssj.probdist.PiecewiseLinearEmpiricalDist.PiecewiseLinearEmpiricalDist ( Reader in ) throws IOException

Constructs a new empirical distribution using the observations read from the reader in.

This constructor will read the first double of each line in the stream. Any line that does not start with a +, -, or a decimal digit, is ignored. The file is read until its end. One must be careful about lines starting with a blank. This format is the same as in UNURAN.

Definition at line 88 of file PiecewiseLinearEmpiricalDist.java.