﻿ 000292_Calculation of Probability Density Function and cumulative distribution function※normal distribution.

# Calculation of Probability Density Function and Cumulative Distribution Function ※Normal distribution(Gaussian distribution).

## Keyword

Probability Density Function,PDF,Cumulative Distribution Function,CDF,Normal distribution,Gaussian distribution,Mean,Standard deviation.

## Reference

・『METHODS OF MATHEMATICAL PHYSICS』(SIR HAROLD JEFFREYS,BERTHA SWIRLES).
・『THE CALCULUS OF OBSERVATIONS』(SIR EDMUND WHITTAKER,G.ROBINSON).
・『Handbook of Mathematical Functions with Formulas,Graphs,and Mathematical Tables』(MILTON ABRAMOWITZ,IRENE A.STEGUN).
・『統計分布ハンドブック』（蓑谷千凰彦）.

## Remarks

・Cumulative Distribution Function is calculated by integration of Probability Density Function using Simpson's rule.Therefore,it contains error.CDF(μ) doesn't become exactly 0.5 as an example in this page.In addition to that,CDF that are smaller than minus6σ is calculated as 0 in this page.
・Simpson's rule:∫[x0～x2]f(x)≈h/3*[f(x0)+4*f(x1)+f(x2)].h=(x2-x0)/2.x1=(x0+x2)/2.
・pdf=1/((2*π)0.5*σ)*exp[-1/(2*σ2)*(x-μ)2].

## History

・2009/06/20：BugFix.Fixing about calculation of CDF.
・2009/06/18：Function addition:Function to change the Number of Partitions dividing the Standard deviation.To enlarge this number(n),more accurate result of CDF will be obtained,but the time needed for the calculation becomes long.
・2009/06/17：Display both Probability Density Function and Cumulative Distribution Function.
・2009/06/16：Function addition:Calculation of Cumulative Distribution Function.
・2009/06/16：Correction of Page Title.