ideation.NormalDistribution Class Reference

Implements the standard and non standard probability density function (pdf) and cumulative distribution function (cdf) for normal distributions. More...

List of all members.

Static Public Member Functions
static double	pdf (double mean, double variance, double x)
	The probabability density function at point x of the normal distribution.
static double	cdf1 (double x)
	Approximation of the standard cumulative density function of the normal distribution.
static double	erf (double x)
	Approximation of the error function according to Winitzki.
static double	cdf (double mean, double variance, double x)
	Approximation of the cumulative density function of the normal distribution.
static void	main (String args[])
	test: Tests for Normal Distributions...
Static Public Attributes
static final double	b0 = 0.2316419
	Parameter for Abramovitz Stegun Method.
static final double	b1 = 0.319381530
	Parameter for Abramovitz Stegun Method.
static final double	b2 = -0.356563782
	Parameter for Abramovitz Stegun Method.
static final double	b3 = 1.781477937
	Parameter for Abramovitz Stegun Method.
static final double	b4 = -1.821255978
	Parameter for Abramovitz Stegun Method.
static final double	b5 = 1.330274429
	Parameter for Abramovitz Stegun Method.

---

Detailed Description

Accuracies:

• The probability density function (pdf) is accurate to double precision.
• The cumulative density function (cdf) is approximated numerically without iteration for maximum efficiency and is only accurate to five or six significant figures.

Uses approximations by Abramovitz and Stegun http://www.math.sfu.ca/~cbm/aands/page_932.htm and Sergeij Winitzki http://www.scribd.com/doc/82414963/Winitzki-Approximation-to-Error-Function

Author:

Ruediger Ruwe <ruediger.ruwe @ rwth-aachen.de>

Version:

1.0

Since:

10.08.2012

---

Member Function Documentation

static double ideation.NormalDistribution.cdf	(	double	mean,
		double	variance,
		double	x
	)		[static]

Uses the approximations used by ideation.NormalDistribution#cdf1

Parameters:

mean	mean
variance	variance (sigma)^2
x	x

Returns:

cdf(x)

static double ideation.NormalDistribution.cdf1

(

double

x

)

[static]

• for positive x use very accurate Abramovitz and Stegun method. (direct)
• for negative x use error function. (indirect) ideation.NormalDistribution#erf

Parameters:

x

Returns:

pdf(x)

static double ideation.NormalDistribution.erf

(

double

x

)

[static]

The accuracy could be higher (about 5-6 significant figures) but there are no iterations needed which will provide a decent efficiency.

Parameters:

x

x

Returns:

erf(x)

static void ideation.NormalDistribution.main

(

String

args[]

)

[static]

Uses the approximations used by ideation.NormalDistribution#cdf1

For test purposes you can enter the package in this class and check the output with other calculations.

static double ideation.NormalDistribution.pdf	(	double	mean,
		double	variance,
		double	x
	)		[static]

Parameters:

mean	mean
variance	variance (sigma^2)
x	point of interest

Returns:

pdf(x)

---

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

• NormalDistribution.java