Probability Integral
Probability Integral :
Also called: error function, erf: The classical form (still widely used in engineering work) of the definite integral of the special normal distribution for which the mean fj. = 0 and standard deviation cr = 1/V~2. Geometrically, the probability integral equals the area under this density curve between -z and z, where z is an arbitrary positive number. Often denoted by the symbol erf z (read "error function of z") the probability integral is defined thus: erf z = -2- fZ e~x2dx. Modern statistical usage favors the unit normal variate u, which is such that p = 0 and a = 1. The relation between the probability integral erf z and the distribution function F(u) of the unit normal variate u is as follows u positive: F(u) = i- + 1 erf (uffl), u negative: F(u) = 1 -1 erf (-uffl). See unit normal distribution. N.B. Refer to source to verify equation(s)
