Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential entropies. A general result for the desired differential entropy convergence is provided, taking into account both compactly and uncompactly supported densities....

 Many Limit Theorems, Convergence Theorems and Characterization Theorems in Probability and Statistics, in particular those related to normal distribution , are based on the assumption of independence of two or more random variables. However, the full power of independence is not used in the proofs of these Theorems, since it is the distribution of summation of the random variables whic...

Earthquake time history records are required to perform dynamic nonlinear analyses. In order to provide a suitable set of such records, they are scaled to match a target spectrum as introduced in the well-known design codes. Corresponding scaling factors are taken similar in practice however, optimizing them reduces extra-ordinary economic charge for the seismic design. In the present work a ne...