Parametric Weighting Functions

This paper provides behavioral foundations for parametric weighting functions under rankdependent utility. This is achieved by decomposing the independence axiom of expected utility into separate meaningful properties. These conditions allow us to characterize rank-dependent utility with power and exponential weighting functions. Moreover, by restricting the conditions to subsets of the probability interval, foundations of rank-dependent utility with parametric inverse-S shaped weighting functions are obtained. --Comonotonic independence,probability weighting function,preference foundation,rank-dependent utility

Nonparametric estimation when income is reported in bands and at points

We show how to estimate kernel density functions of distributions in which some of the responses are provided in brackets, by inverse probability weighting. We consider two cases, one where the data are CAR and where the data are not CAR. We show how the selection probabilities can be estimated by means of the EM algorithm without specifying a parametric distribution function for the variable. A Monte Carlo experiment shows that this procedure estimates the selection parameters fairly precisely. We apply these techniques to earnings data from South Africa’s first post-apartheid nationally representative survey, the 1994 October Household Survey.coarsening, bracket responses, EM algorithm, inverse probability weighting

The Pearson system of utility functions

This paper describes a parametric family of utility functions for decision analysis. The parameterization is obtained by embedding the HARA class in a four-parameter representation for the risk aversion function. The resulting utility functions have only four shapes: concave, convex, S-shaped, and reverse S-shaped. This makes the family suited for both expected utility and prospect theory. We also describe an alternative technique to estimate the four parameters from elicited utilities, which is simpler and easier to implement than standard fitting by minimization of the mean quadratic error.coefficient of risk aversion, elicitation of preferences under risk, expected utility, HARA utility functions, Pearson system of distributions, prospect theory, probability weighting function, target- based decisions.

A rank-dependent utility model of uncertain lifetime, time consistency and life insurance

In a continuous time life cycle model of consumption with uncertain lifetime and no ''pure time preference", we use a non-parametric specification of rank dependent utility theory to characterize the preferences of the agents. From normative point of view, the paper discusses the implication of adding an axiom of time consistency to the former model. We prove that time consistency holds for a much wider class of probability weighting functions than the identity one characterizing the expected utility model. This special class of probability weighting functions provides foundations for a constant subjective rate of discount which interact multiplicatively with the instantaneous conditional probability of dying. We show that even if agent are time consistent, life annuities no more provide perfect insurance against the risk to live

Design of combined robust controller for a pneumatic servo actuator system with uncertainty

In this paper the position control design of a pneumatic servo actuator system using a combined H-inf /QFT technique is presented. First, an H-inf controller is designed to assure robust stability for the system. Particle swarm optimization (PSO) algorithm is used to tune the weighting functions. This method is used to find the optimal values of weighting functions parameters that lead to obtain an optimal H-inf-controller by minimizing the infinity norm of the transfer function of the nominal closed loop system. The quantitative feedback theory (QFT) is used to enhance the closed loop system performance. A multiplicative unstructured model extracted from the parametric uncertainty is used for control design. Finally, the simulation results are presented and compared with previous work

Robust LPV Control for Attitude Stabilization of a Quadrotor Helicopter under Input Saturations

This article investigates the robust stabilization of the rotational subsystem of a quadrotor against external inputs (disturbances, noises, and parametric uncertainties) by the LFT-based LPV technique. By establishing the LPV attitude model, the LPV robust controller is designed for the system. The weighting functions are computed by Cuckoo Search, a meta-heuristic optimization algorithm. Besides, the input saturations are also taken into account through the Anti-Windup compensation technique. Simulation results show the robustness of the closed-loop system against disturbances, measurement noises, and the parametric uncertainties

A Generalized Convolution Model and Estimation for Non-stationary Random Functions

Standard geostatistical models assume second order stationarity of the underlying Random Function. In some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In this paper, we introduce a new model for second order non-stationary Random Functions as a convolution of an orthogonal random measure with a spatially varying random weighting function. This new model is a generalization of the common convolution model where a non-random weighting function is used. The resulting class of non-stationary covariance functions is very general, flexible and allows to retrieve classes of closed-form non-stationary covariance functions known from the literature, for a suitable choices of the random weighting functions family. Under the framework of a single realization and local stationarity, we develop parameter inference procedure of these explicit classes of non-stationary covariance functions. From a local variogram non-parametric kernel estimator, a weighted local least-squares approach in combination with kernel smoothing method is developed to estimate the parameters. Performances are assessed on two real datasets: soil and rainfall data. It is shown in particular that the proposed approach outperforms the stationary one, according to several criteria. Beyond the spatial predictions, we also show how conditional simulations can be carried out in this non-stationary framework.Comment: 24 pages, 10 figures, 2 table

M[pi]log, Macromodeling via parametric identification of logic gates

This paper addresses the development of computational models of digital integrated circuit input and output buffers via the identification of nonlinear parametric models. The obtained models run in standard circuit simulation environments, offer improved accuracy and good numerical efficiency, and do not disclose information on the structure of the modeled devices. The paper reviews the basics of the parametric identification approach and illustrates its most recent extensions to handle temperature and supply voltage variations as well as power supply ports and tristate devices