Calculation of Probability Density Function and Cumulative Distribution Function
※Log Normal distribution.

Keyword

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

Reference

・『統計分布ハンドブック』(蓑谷千凰彦).
・『新版数値計算ハンドブック』(大野豊・磯田和男).
WIKIPEDIA.

Remarks

・Cumulative Distribution Function is calculated by Approximation of Error function.Therefore,it contains error.
・Cumulative Distribution Function=1/2+1/2*erf((Ln(x)-μ)/(σ*2^0.5)).
・pdf=1/((2*π)0.5*σ*x)*exp[-1/(2*σ2)*(Ln(x)-μ)2].
・Error function:erf(x)≈1-1/(1+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5+a6*x^6)^16.
 a1=0.0705230784
 a2=0.0422820123
 a3=0.0092705272
 a4=0.0001520143
 a5=0.0002765672
 a6=0.0000430638

History

・2009/06/25:BugFix.Fixing about calculation of CDF.
・2009/06/20:BugFix.Fixing about calculation of CDF.
・2009/06/19:Upload.