atanh(x), x REAL or a structure with REAL components |

atanh(x) returns the inverse hyperbolic tangent of the elements of x, when x is a REAL scalar, vector, matrix or array. The result has the same shape as x. In terms of other functions, atanh(x) = .5*log((1+x)/(1-x)). This transform is sometimes called the Fisher z-transform. When r is a sample Pearson correlation from a bivariate normal sample of size N and population correlation rho, atanh(r) is approximately normal with mean rho and variance 1/(N-2). When any element of x is MISSING, so is the corresponding element of atanh(x). When any element of x >= 1 or <= -1, the corresponding element of atanh(x) is MISSING. In both cases a warning message is printed. When x is a structure, all of whose non-structure components are REAL, atanh(x) is a structure of the same shape and with the same component names as x, with each non-structure component transformed by atanh(). See topic 'transformations' for more information on atanh().

Gary Oehlert 2003-01-15