This paper introduces a framework for robustifying convex, law invariant risk measures, to deal with ambiguity of the distribution of random asset losses in portfolio selection problems. The robustified risk measures are defined as the worst-case portfolio risk over the ambiguity set of loss distributions, where an ambiguity set is defined as a neighborhood around a reference probability measur...

The measure of entropy introduced by Shannon [12] is the key concept in the literature of information theory and has found tremendous applications in different disciplines of science and technology. The various researchers have generalized this entropy with different approaches. The object of the present manuscript is to develop a generalized measure of entropy by using the property of concavit...

The paper considers parametric uncertain systems of the form ẋ t Mx t ,M ∈ M,M ⊂ Rn×n, where M is either a convex hull, or a positive cone of matrices, generated by the set of vertices V {M1,M2, . . . ,MK} ⊂ Rn×n. Denote by μ‖ ‖ the matrix measure corresponding to a vector norm ‖ ‖. When M is a convex hull, the condition μ‖ ‖ Mk ≤ r < 0, 1 ≤ k ≤ K, is necessary and sufficient for the existence ...

Likert, Likert-type, and ordinal-scale responses are very popular psychometric item scoring schemes for attempting to quantify people's opinions, interests, or perceived efficacy of an intervention and are used extensively in Physical Education and Exercise Science research. However, these numbered measures are generally considered ordinal and violate some statistical assumptions needed to eval...

8 Empirical illustrations 11 8.1 The software R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 8.2 Non parametric estimation of densities . . . . . . . . . . . . . . . . . . . . . . . 12 8.3 Estimation of the mean and of the welfare . . . . . . . . . . . . . . . . . . . . . 13 8.4 Inequality measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 ...

A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, all based on a nonstandard action of vector fields on functions. There is a n...

OBJECTIVE To investigate whether using a parametric statistic in comparing groups leads to different conclusions when using summative scores from rating scales compared with using their corresponding Rasch-based measures. METHODS A Monte Carlo simulation study was designed to examine between-group differences in the change scores derived from summative scores from rating scales, and those der...

This paper uses the 2001 wave of National Drug Strategy Household Survey (NDSHS) to assess the impact of marijuana decriminalization policy on marijuana smoking prevalence in Australia. Both parametric and non-parametric methods are used. The parametric approach postulates an endogenous probit switching model and its nested binary probit, endogenous bivariate probit and two-part models to estim...

In this paper, we consider structure preserving measure transforms for time-changed Lévy processes. Within this class of transforms preserving the time-changed Lévy structure, we derive equivalent martingale measures minimizing relative q-entropy. Structure preservation is found to be an inherent property of minimal q-entropy martingale measures under continuous time changes, whereas it imposes...