A variant of the class NormalDist (for the normal distribution with mean \(\mu\) and variance \(\sigma^2\)). More...
Inheritance diagram for NormalDistQuick:
Collaboration diagram for NormalDistQuick:
Public Member Functions | |
| NormalDistQuick () | |
Constructs a NormalDistQuick object with default parameters \(\mu= 0\) and \(\sigma= 1\). | |
| NormalDistQuick (double mu, double sigma) | |
Constructs a NormalDistQuick object with mean \(\mu\) = mu and standard deviation \(\sigma\) = sigma. | |
| 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... | |
 Public Member Functions inherited from NormalDist | |
| NormalDist () | |
Constructs a NormalDist object with default parameters \(\mu= 0\) and \(\sigma= 1\). | |
| NormalDist (double mu, double sigma) | |
Constructs a NormalDist object with mean \(\mu\) = mu and standard deviation \(\sigma\) = 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 \(\mu\). | |
| double | getSigma () |
| Returns the parameter \(\sigma\). | |
| void | setParams (double mu, double sigma) |
| Sets the parameters \(\mu\) and \(\sigma\) of this object. | |
| double [] | getParams () |
| Return a table containing the parameters of the current distribution. More... | |
| 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 | cdf01 (double x) |
| Same as cdf(0.0, 1.0, x). | |
| static double | cdf (double mu, double sigma, double x) |
| Returns an approximation of \(\Phi(x)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance 1. More... | |
| static double | barF01 (double x) |
| Same as barF(0.0, 1.0, x). | |
| static double | barF (double mu, double sigma, double x) |
| Returns an approximation of \(1 - \Phi(x)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance. More... | |
| static double | inverseF01 (double u) |
| Same as inverseF(0.0, 1.0, u). | |
| static double | inverseF (double mu, double sigma, double u) |
| Returns an approximation of \(\Phi^{-1}(u)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance 1. More... | |
| Static Public Member Functions inherited from NormalDist | |
| static double | density01 (double x) |
| Same as density(0, 1, x). | |
| static double | density (double mu, double sigma, double x) |
| Computes the normal density function ( fnormal ). | |
| static double | cdf01 (double x) |
| Same as cdf(0, 1, x). | |
| static double | cdf (double mu, double sigma, double x) |
| Computes the normal distribution function with mean \(\mu\) and variance \(\sigma^2\). More... | |
| static double | barF01 (double x) |
| Same as barF(0, 1, x). | |
| static double | barF (double mu, double sigma, double x) |
| Computes the complementary normal distribution function \(\bar{F}(x) = 1 - \Phi((x-\mu)/\sigma)\), with mean \(\mu\) and variance \(\sigma^2\). More... | |
| static double | inverseF01 (double u) |
| Same as inverseF(0, 1, u). | |
| static double | inverseF (double mu, double sigma, double u) |
| Computes the inverse normal distribution function with mean \(\mu\) and variance \(\sigma^2\). More... | |
| static double [] | getMLE (double[] x, int n) |
| Estimates the parameters \((\mu, \sigma)\) of the normal distribution using the maximum likelihood method, from the \(n\) observations \(x[i]\), \(i = 0, 1,…, n-1\). More... | |
| static NormalDist | getInstanceFromMLE (double[] x, int n) |
| Creates a new instance of a normal 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 \(E[X] = \mu\) of the normal distribution with parameters \(\mu\) and \(\sigma\). More... | |
| static double | getVariance (double mu, double sigma) |
| Computes and returns the variance \(\mbox{Var}[X] = \sigma^2\) of the normal distribution with parameters \(\mu\) and \(\sigma\). More... | |
| static double | getStandardDeviation (double mu, double sigma) |
| Computes and returns the standard deviation \(\sigma\) of the normal distribution with parameters \(\mu\) and \(\sigma\). More... | |
Additional Inherited Members | |
| Public Attributes inherited from ContinuousDistribution | |
| int | decPrec = 15 |
| Protected Attributes inherited from NormalDist | |
| double | mu |
| double | sigma |
| Protected Attributes inherited from ContinuousDistribution | |
| double | supportA = Double.NEGATIVE_INFINITY |
| double | supportB = Double.POSITIVE_INFINITY |
| Static Protected Attributes inherited from NormalDist | |
| static final double | RAC2PI = 2.50662827463100050 |
| Static Protected Attributes inherited from ContinuousDistribution | |
| static final double | XBIG = 100.0 |
| static final double | XBIGM = 1000.0 |
| static final double [] | EPSARRAY |
Detailed Description
A variant of the class NormalDist (for the normal distribution with mean \(\mu\) and variance \(\sigma^2\)).
The difference is in the implementation of the methods cdf01, barF01 and inverseF01, which are faster but less accurate than those of the class NormalDist.
Member Function Documentation
◆ barF() [1/2]
| 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.
◆ barF() [2/2]
|
static |
Returns an approximation of \(1 - \Phi(x)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance.
- Uses Marsaglia et al’s [174] fast method with table lookups. Returns 15 decimal digits of precision. This method is approximately twice faster than
NormalDist.barF.
◆ cdf() [1/2]
| 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.
◆ cdf() [2/2]
|
static |
Returns an approximation of \(\Phi(x)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance 1.
Uses Marsaglia et al’s [174] fast method with table lookups. Returns 15 decimal digits of precision. This method is approximately 60% faster than NormalDist.cdf.
◆ inverseF() [1/2]
| 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.
◆ inverseF() [2/2]
|
static |
Returns an approximation of \(\Phi^{-1}(u)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance 1.
Uses the method of Marsaglia, Zaman, and Marsaglia [174] , with table lookups. Returns 6 decimal digits of precision. This method is approximately 20% faster than NormalDist.inverseF.
The documentation for this class was generated from the following file:
- NormalDistQuick.java
