Calculation of Probability Density Function and Cumulative Distribution Function
※Chi-square distribution.

Keyword

Probability Density Function,PDF,Cumulative Distribution Function,CDF,Chi-square distribution,Gamma function,Upper incomplete gamma function,Lower incomplete gamma function,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

・pdf=(1/2)^(k/2)/Γ(k/2)*x^(k/2-1)*e^(-x/2).
・cdf=γ(k/2,x/2)/Γ(k/2).
・erf(x)≈2/π^0.5*∫[0~x]e^(-u^2)・du≈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

・2009/06/29:Upload.