A new approach for point process diagnostics is presented. The method is based on extending second-order statistics for point processes by weighting each point by the inverse of the conditional intensity function at the point’s location. The result is generalized versions of the spectral density, R/S statistic, correlation integral and K-function, which can be used to test the fit of a complex ...

Necessary and sufficient conditions for the weak convergence of the generalized and the dual generalized extremal quotient are obtained. The class of possible nondegenerate limit distribution functions of quotient of generalized and its dual extreme order statistics is characterized. Some illustrative examples are obtained.