Keyword
Probability Density Function,PDF,Cumulative Distribution Function,CDF,Normal
distribution,Gaussian distribution,Mean,Standard deviation.
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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).
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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].
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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.
・2009/06/15:Upload.
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