Distribution In Terms Of Moments Research Articles

Recent trends in employees’ earnings inequality in Portugal: A quantitative analysis between 1986 and 2017

This paper examines employees? earnings inequality in Portugal for 1986-2017 using data from the Personnel Records database. Our objective is twofold: (a) characterize earnings inequality by comparing representative distributions, before and after the great crisis; and (b) investigate the role played by the business cycle on the behaviour of earnings inequality by estimating Autoregressive Distributed Lag (ADL) models. To identify trends and variations along the trend in earnings inequality we use cardinal measures and the coefficient of variation. We inspect the characteristics of earnings distributions in terms of moments (mean and median) and polarization (using relative distributions analysis). The main findings are: (1) earnings inequality shows a positive trend (except during the great crisis); (2) polarization is present in every year, with lower polarisation prevailing over upper polarization, both evolving at different paces (very fast 1989-2002; slower pace 2002-2008; negative growth 2008-2017); (3) the business cycle relationship with earnings inequality is negative.

Option-Implied Objective Measures of Market Risk

Foster and Hart (2009) introduce an objective measure of the riskiness of an asset that implies a bound on how much of one’s wealth is ‘safe’ to invest in the asset while (a.s.) guaranteeing no-bankruptcy. In this study, we translate the Foster-Hart measure from static and abstract gambles to dynamic and applied finance using nonparametric estimation of risk-neutral densities from S&P 500 call and put option prices covering 2003 to 2013. The dynamics of the resulting ‘option-implied Foster-Hart bound’ are assessed in light of other well-known option-implied risk measures including value at risk, expected shortfall and risk-neutral volatility, as well as high moments of the densities and several industry measures. Rigorous variable selection reveals that the new measure is a significant predictor of (large) ahead-return downturns. Furthermore, it grasps more characteristics of the risk-neutral probability distributions in terms of moments than other measures and exhibits predictive consistency. The robustness of the risk-neutral density estimation is analyzed via Monte Carlo methods.

Goodness-of-fit tests via characterizations. Special cases

We give goodness-of-fit tests for exponential, Weibull, extreme–value, logistic, normal, and Cauchy distributions. They are derived from characterization conditions of continuous distributions in terms of moments of the k-th record values. U-statistics are used to estimate the associated expectations.

Hydro energy management optimization in a deregulated electricity market

When electricity prices were regulated, hydropower optimization often considered only the inflow uncertainty. In a deregulated electricity market, price uncertainty must be also considered in addition to inflow uncertainty. This makes the operation problem more challenging due to inclusion of the objective of minimizing risk. It also makes the objective function nonlinear while the estimation of risk is problematic. For dealing with uncertainty, a set of finite scenarios of inflow or price sequences may form the evolution of information over the stages that are used in optimization algorithms. Such implicit optimization methods can be seen as an extension of deterministic optimization. A disadvantage is the number of scenarios may grow exponentially in multi-stage optimization problems, even with only a few branches at each stage. An explicit method, denoted as the Fletcher-Ponnambalam model (FP), has been recently developed for the first and second moments of the storage state distributions in terms of moments of the inflow distributions. This method provides statistical information on the nature of random behaviour of the system state variables without any discretization and hence suitable for multireservoir problems. Also not considering scenarios makes it computationally inexpensive, as there is little growth to the size of the original problem. In this paper, we introduce the price uncertainty into the FP model; our results indicate that the method could achieve optimum policy considering also the reduction of risk, using the second moment information. Our study is for medium term operations of a single reservoir. The results are compared with corresponding results from simulation and where possible, with the well-known Benders' Decomposition method (BD).

On Characterizations of the Double Exponential Distribution in Terms of Moments of Order Statistics

On Characterizations of the Double Exponential Distribution in Terms of Moments of Order Statistics

Stochastic control for risk under deregulated electricity market — a case study using a new formulation

This paper describes the implementation of a new solution approach — Fletcher-Ponnambalam model (FP) — for risk management in hydropower system under deregulated electricity market. The FP model is an explicit method developed for the first and second moments of the storage state distributions in terms of moments of the inflow distributions. This method provides statistical information on the nature of random behaviour of the system state variables without any discretization and hence suitable for multi-reservoir problems. Also avoiding a scenario-based optimization makes it computationally inexpensive, as there is little growth to the size of the original problem. In this paper, the price uncertainty was introduced into the FP model in addition to the inflow uncertainty. Lake Nipigon reservoir system is chosen as the case study and FP results are compared with the stochastic dual dynamic programming (SDDP). Our studies indicate that the method could achieve optimum operations, considering risk minimization as one of the objectives in optimization.Key words: reservoir operations, explicit method, uncertainty, stochastic programming, risk.

On characterizations of continuous distributions in terms of moments of order statistics when the sample size is random

We characterize continuous distribution functions F of a population when the sample size N is a random variable. Characterizing conditions in terms of moments of the kth order statistics are given, among other things, for the uniform, exponential, Pareto, logistic, and Weibull distributions.

Particle identification with neural networks using a rotational invariant moment representation

A feed-forward neural network is used to identify electromagnetic particles based upon their showering properties within a segmented calorimeter. The novel feature is the expansion of the energy distribution in terms of moments of the so-called Zernike functions which are invariant under rotation. The multidimensional input distribution for the neural network is transformed via a principle component analysis and rescaled by its respective variances to ensure input values of the order of one. This results is a better performance in identifying and separating electromagnetic from hadronic particles, especially at low energies.

Characterization of continuous distributions in terms of moments of extremal statistics

We give characterizations of continuous distributions in terms of moments of order statistics when the sample size is random. In particular, we characterize uniform, exponential, Pareto, and logistic distributions. Special cases of a random sample size (logarithmic series, geometrical, truncated binomial, truncated negative binomial, and truncated Poisson distribution) are also considered.