Gaussian Distribution

Table of Contents

Probability density function

  • XN(μ,σ2)

    p(x)=12πσexp[(xμ)22σ2]

Distribution function

  • Q-function
    • Definition

      Q(x)x12πexp(x22)dx
    • Properties

      Q(x)+Q(x)=1Q(0)=12
  • Error function and complementary error function
    • Definitions

      erf(x)2π0xexp(x2)dxerfc(x)2πxexp(x2)dx
    • Properties

      erf(x)+erfc(x)=1erf(x)=12Q(2x)erfc(x)=2Q(2x)