User:Asitgoes/Normdis
Developer(s) | Institute for Land Reclamation and Improvement (ILRI) |
---|---|
Written in | Delphi |
Operating system | Microsoft Windows |
Available in | English |
Type | Statistical software |
License | Proprietary Freeware |
Website | NormDis |
In statistics and data analysis the application software NormDis is a free and user-friendly calculator for the determination of the cumulative probability Pc(Xr) for any random variable (X) following the normal distribution. Here, the cumulative probability Pc(Xr) stands for the probability P that X is less than a reference value Xr of X. Biefly : Pc(Xr) = P(X<Xr).
Reversely, the calculator can give the value of Xr given Pc. Hence, it is a two-way calculator. The data required are the mean and the standard deviation of the distribution of X.
Intervals
![](http://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/220px-Standard_deviation_diagram.svg.png)
The probability (Pi) that X occurs in an interval between an upper limit (U) and a lower limit (L) can be found from:
- Pi = P(L<X<U) = Pc(U) - Pc(L) .
Thus, using the calculator twice, namely for Xr=U and Xr=L, and subtracting the results, one finds the value of Pi that L<X<U.
Numerical method
The cumulative distribution function of the normal distribution cannot be calculated analytically and a numerical approximation has to be used. NormDis uses the Hastings method,[1] as follows :
where
and
- b0 = 0.2316419, b1 = 0.319381530, b2 = −0.356563782, b3 = 1.781477937, b4 = −1.821255978, b5 = 1.330274429.
Here, is the standard normal probability density function (PDF):
When the distribution is standard normal, one can use = Xr, otherwise = (Xr - M) / S, where M is the mean and S the standard deviation.
Graphics
The NormDis program provides graphics for the various values computed with the calculator. See the examples to left and right.
References
- ^ Zelen, Marvin; Severo, Norman C. (1964). Probability Functions (chapter 26). Handbook of mathematical functions with formulas, graphs, and mathematical tables, by Abramowitz, M.; and Stegun, I. A.: National Bureau of Standards. New York, NY: Dover. ISBN 0-486-61272-4.
Category:Statistical software
Category:Data analysis software
Category:Freeware