Supermodular comparison of dependence models and multivariate processes, with applications

The supermodular order is a well-known tool to compare the intrinsic degree of dependence between random vectors or multivariate processes. In this note we describe a general framework for the supermodular comparisons of models incorporating individual and common factors. Examples are given on how to apply these models in comparing hitting times for multivariate processes of interest within risk analysis and reliability theory

Subjective and objective assessment of acoustical and overall environmental quality in secondary school classrooms

A subjective survey on perceived environmental quality has been carried out on 51 secondary-school classrooms, some of which have been acoustically renovated, and acoustical measurements were carried out in eight of the 51 classrooms, these eight being representative of the different types of classrooms that are the subject of the survey. A questionnaire, which included items on overall quality and its single aspects such as acoustical, thermal, indoor air and visual quality, has been administered to 1006 students. The students perceived that acoustical and visual quality had the most influence on their school performance and, with the same dissatisfaction for acoustical, thermal and indoor air quality, they attributed more relevance, in the overall quality judgment, to the acoustical condition. Acoustical quality was correlated to speech comprehension, which was correlated to the speech transmission index, even though the index does not reflect all the aspects by which speech comprehension can be influenced. Acoustical satisfaction was lower in nonrenovated classrooms, and one of the most important consequences of poor acoustics was a decrease in concentration. The stronger correlation between average noise disturbance scores and LA max levels, more than LAeq and LA90, showed that students were more disturbed by intermittent than constant noise

Stochastic Comparisons for Time Transformed Exponential Models

Different sufficient conditions for stochastic comparisons between random vectors have been described in the literature. In particular, conditions for the comparison of random vectors having the same copula, i.e., the same dependence structure, may be found in Müller and Scarsini (2001). Here we provide conditions for the comparison, in the usual stochastic order sense and in other weaker stochastic orders, of two time transformed exponential bivariate lifetimes having different copulas. Some examples of applications are provided too

Portfolio selection through an extremality stochastic order

In this paper, we introduce a new multivariate stochastic order that compares random vectors in a direction which is determined by a unit vector, generalizing the previous upper and lower orthant orders. The main properties of this new order, together with its relationships with other multivariate stochastic orders, are investigated and, we present some examples of application in the determination of optimal allocations of wealth among risks in single period portfolio problem

A characterization of the multivariate excess wealth ordering

In this paper, some new properties of the upper-corrected orthant of a random vector are proved. The univariate right-spread or excess wealth function, introduced by Fernández-Ponce et al. (1996), is extended to multivariate random vectors, and some properties of this multivariate function are studied. Later, this function was used to define the excess wealth ordering by Shaked and Shanthikumar (1998) and Fernández-Ponce et al. (1998). The multivariate excess wealth function enable us to define a new stochastic comparison which is weaker than the multivariate dispersion orderings. Also, some properties relating the multivariate excess wealth order with stochastic dependence are describe

On a new NBUE property in multivariate sense: an application

Since multivariate lifetime data frequently occur in applications, various properties of multivariate distributions have been previously considered to model and describe the main concepts of aging commonly considered in the univariate setting. The generalization of univariate aging notions to the multivariate case involves, among other factors, appropriate definitions of multivariate quantiles and related notions, which are able to correctly describe the intrinsic characteristics of the concepts of aging that should be generalized, and which provide useful tools in the applications. A new multivariate version of the well-known New Better than Used in Expectation univariate aging notion is provided, by means of the concepts of the upper corrected orthant and multivariate excess-wealth function. Some of its properties are described, with particular attention paid to those that can be useful in the analysis of real data sets. Finally, through an example it is illustrated how the new multivariate aging notion influences the final results in the analysis of data on tumor growth from the Comprehensive Cohort Study performed by the German Breast Cancer Study Grou

A Brownian Model for Crystal Nucleation

In this work a phenomenological stochastic differential equation is proposed to model the time evolution of the radius of a pre-critical molecular cluster during nucleation (the classical order parameter). Such a stochastic differential equation constitutes the basis for the calculation of the (nucleation) induction time under Kramers' theory of thermally activated escape processes. Considering the nucleation stage as a Poisson rare-event, analytical expressions for the induction time statistics are deduced for both steady and unsteady conditions, the latter assuming the semiadiabatic limit. These expressions can be used to identify the underlying mechanism of molecular cluster formation (distinguishing between homogeneous or heterogeneous nucleation from the nucleation statistics is possible) as well as to predict induction times and induction time distributions. The predictions of this model are in good agreement with experimentally measured induction times at constant temperature, unlike the values obtained from the classical equation, but agreement is not so good for induction time statistics. Stochastic simulations truncated to the maximum waiting time of the experiments confirm that this fact is due to the time constraints imposed by experiments. Correcting for this effect, the experimental and predicted curves fit remarkably well. Thus, the proposed model seems to be a versatile tool to predict cluster size distributions, nucleation rates, (nucleation) induction time and induction time statistics for a wide range of conditions (e.g. time-dependent temperature, supersaturation, pH, etc.) where classical nucleation theory is of limited applicability.Comment: 20 pages, 3 figure