Understanding the Normal Distribution for Real

Other symmetric unimodal distributions are (ignoring normalization constants) the generalized error distribution exp(-|x|^c) (Normal for c=2, Laplace for c=1) and the hyperbolic secant distribution 1/(exp(x) + exp(-x)). They decay as exp(-x) in the tails, more slowly than exp(-x^2) for the normal. The Student's t distribution have even fatter tails, decaying as x^(-p) in the tails, where the the value of p depends on the number of degrees of freedom.