CHAPTER 13 - Probability Integrals and the Error Function

Abstract

This chapter discusses the probability integrals and the error function. It describes the normal or Gaussian probability density function. When the normal probability density f(x) is standardized with zero mean (μ = 0) and unit variance (σ = 1) the normal probability distribution P(x), also denoted by Φ(x), is defined. The error function erf x occurs in probability theory and statistics and diffusion problems. The complementary error function erfc x is also described in the chapter.