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., [118] (page 318)). More...
Public Member Functions | |
| PiecewiseLinearEmpiricalDist (double[] obs) | |
Constructs a new piecewise-linear distribution using all the observations stored in obs. More... | |
| PiecewiseLinearEmpiricalDist (Reader in) throws IOException | |
Constructs a new empirical distribution using the observations read from the reader in. More... | |
| 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. | |
| 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 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... | |
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 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., [118] (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 \(i=1,…,n-1\).
Constructor & Destructor Documentation
◆ PiecewiseLinearEmpiricalDist() [1/2]
| 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.
◆ PiecewiseLinearEmpiricalDist() [2/2]
| 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.
Member Function Documentation
◆ barF()
| double barF | ( | double | x | ) |
Returns \(\bar{F}(x) = 1 - F(x)\).
- Parameters
-
x value 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
-
x value at which the distribution function is evaluated
- Returns
- distribution function evaluated at
x
Implements Distribution.
◆ inverseF()
| double inverseF | ( | double | u | ) |
Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).
- Parameters
-
u value 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:
- PiecewiseLinearEmpiricalDist.java
