The main topic of this lecture will be the study of the distribution function of additive arithmetical functions. Before proceeding with the subject I want to call attention to the excellent review of Kac 13 on this subject, were a very clear and detailed discussion of the interplay of probability and number theory is given. In the present review I try to emphasize those results which were not ...

This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of convergence. The model contains the generalized additive model with unknown link function as a special case. For this case, it is shown that the additive components and...

As a flexible alternative to the Cox model, the additive risk model assumes that the hazard function is the sum of the baseline hazard and a regression function of covariates. For right censored survival data when variable selection is needed along with model estimation, we propose a path consistent model selector using a modified Lasso approach, under the additive risk model assumption. We sho...

A universality ansatz for the contact values of a multicomponent mixture of additive hard spheres is used to propose new formulae for the case of disparate-size binary mixtures. A comparison with simulation data and with a recent proposal by Alawneh and Henderson for binary mixtures shows reasonably good agreement with the predictions for the contact values of the large-large radial distributio...

For images, stochastic resonance or useful-noise effects have previously been assessed with low-level pixel-based information measures. Such measures are not sensitive to coherent spatial structures usually existing in images. As a result, we show that such measures are not sufficient to properly account for stochastic resonance occurring in visual perception. We introduce higher-level similari...

In analogy to ordinary q-additive functions based on q-adic expansions one may use Cantor expansions with a Cantor base Q to define (strongly) Q-additive functions. This paper deals with distribution properties of multi-dimensional sequences which are generated by such Q-additive functions. If in each component we have the same Cantor base Q, then we show that uniform distribution already impli...

BACKGROUND Despite the fact that suicide is an important public health problem, the etiology is still not well understood. Especially lacking is a societal-level approach that takes into account the extent to which several risk factor domains are attributable to new onset of suicidal thoughts and behaviors (STB). METHODS Data stem from a cross-sectional population study of the non-institution...

This note proves that risk measures obtained by applying the equivalent utility principle in rank-dependent utility are additive if and only if the utility function is linear or exponential and the probability weighting (distortion) function is the identity.

New formulas for the multiplicative partition function are developed. Besides giving a fast algorithm for generating these partitions, new identities for additive partitions and the Riemann zeta function are also produced.

A tree functional is called additive if it satisfies a recursion of the form F (T ) = ∑k j=1 F (Bj)+f(T ), where B1, . . . , Bk are the branches of the tree T and f(T ) is a toll function. We prove a general central limit theorem for additive functionals of d-ary increasing trees under suitable assumptions on the toll function. The same method also applies to generalised planeoriented increasin...