Goodness of fit test statistics for the zeta family

Goodness of fit test procedures for the zeta parametric family based on quadratic distances and the Box-Cox transform are developed. Test statistics based on quadratic distances are shown to follow a chi-square distribution asymptotically. Test procedures based on the Box-Cox transform make use of the estimator of the parameter introduced by the Box-Cox transform, and numerical computations are based on the nonlinear weighted least squares algorithms.