de.psychometrica.norming

Class NormalDistribution

java.lang.Object

de.psychometrica.norming.NormalDistribution

public class NormalDistribution
extends java.lang.Object

Java Implementation of the inverse normal distribution function according to the algorithm, defined by Peter John Acklam (pjacklam@online.no) on http://home.online.no/~pjacklam/notes/invnorm/. The license on the page is "Use them as you wish, for whatever purpose." When comparing the precision of the algorithm with the function Microsoft Excel, the mean square sum of deviation between p = .001 and p = .999 amounts to 6,2144E-19. An additional refinement is therefore not necessary for the use in psychometrics. Precompiled binaries and Javadoc can be found at http://www.psychometrica.de/norming.html
The code is licensed under the Lesser General Public License (LGPL 2.0)

Author:

PD Dr. Wolfgang Lenhard; Original algorithm by Peter John Acklam

Constructor Summary

Constructors

Constructor and Description
NormalDistribution()

Method Summary

Methods

Modifier and Type	Method and Description
static double	getCumulativeDistribution(double x) Calculate the normal cumulative density function according to formula 4.5 from Vazquez-Leal, H., Castaneda-Sheissa, R., Filobello-Nino, U., Sarmiento-Reyes, A., & Sanchez Orea, J. (2012).
static double	getInverseCumulativeDistribution(double p)
static double	getNormalDistributionDensity(double z) Calculates the density of the normal distribution function

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

NormalDistribution

public NormalDistribution()

Method Detail

getInverseCumulativeDistribution

public static double getInverseCumulativeDistribution(double p)

Parameters:

p - The probability, e. g. the percent rank in psychodiagnostics

Returns:

the according standardized value, z

getNormalDistributionDensity

public static double getNormalDistributionDensity(double z)

Calculates the density of the normal distribution function

Parameters:

z - the standardized value of a raw value with m = 0.0 and sd = 1.0

Returns:

the density of the normal distribution

getCumulativeDistribution

public static double getCumulativeDistribution(double x)

Calculate the normal cumulative density function according to formula 4.5 from Vazquez-Leal, H., Castaneda-Sheissa, R., Filobello-Nino, U., Sarmiento-Reyes, A., & Sanchez Orea, J. (2012). High Accurate Simple Approximation of Normal Distribution Integral. Mathematical Problems in Engineering, 2012, 1–22. doi:10.1155/2012/124029 The function has a precision of approx. 10E-4, when comparing it to the implementation in MS Excel

Parameters:

x - Standardized value (m = .0, sd = 1.0)

Returns:

cumulative distribution function value; probability, e. g. percent rank