Band 36, Heft 1

In this paper we advance a nonlinear optimization problem for hedging wind power variability by using a dispatchable energy source (DES) like gas. The model considers several important aspects such as modeling of wind power production, electricity price, nonlinear penalization scheme for energy underproduction and interrelations among the considered variables. Results are given in terms of optimal co-generation policy with DES. The optimal policy is interpreted and analyzed in different penalization scenarios and related to a 48 MW hypothetical wind park. The model is suitable for integration of wind energy especially for isolated grids. Some probabilistic results for special moments of a Log-Normal distribution are obtained; they are necessary for the evolution of the optimal policy.

The present work aims to propose an approximation of the sample median distribution with a normal parent distribution. Although the mean is usually used as the central tendency measure for normal samples, the median has also been used in engineering, process control in particular. The proposed method approximates the normal sample median distribution only using the normal distribution function. It outperforms Castagliola’s method for small samples and serves as an alternative approximation for trading off accuracy against computational complexity for large samples.

In this paper, we study one-dimensional backward stochastic differential equations under logarithmic growth in the 𝑧-variable (|z|⁢|ln⁡|z||)(\lvert z\rvert\sqrt{\lvert\ln\lvert z\rvert\rvert}). We show the existence and the uniqueness of the solution when the noise is driven by a Brownian motion and an independent Poisson random measure. In addition, we highlight the connection of such BSDEs with stochastic optimal control problem, where we show the existence of an optimal strategy for the control problem.

Dynamic cumulative residual entropy is a new addition to the class of information measures. In the present paper, we study its relationship with excess wealth transform and derive some identities connecting the two using the quantile-based approach. Some theoretical results that have applications to infer ageing properties and risk measures are presented. These are used as tools to analyse real life data.

Extropy was introduced as a dual complement of the Shannon entropy. In this investigation, we consider failure extropy and its dynamic version. Various basic properties of these measures are presented. It is shown that the dynamic failure extropy characterizes the distribution function uniquely. We also consider weighted versions of these measures. Several virtues of the weighted measures are explored. Finally, nonparametric estimators are introduced based on the empirical distribution function.

Recently, entropy and extropy-based tests for the uniform distribution have attracted the attention of some researchers. This paper proposes nonparametric entropy and extropy estimators based on progressive type-II censoring and investigates their properties and behavior. Performance of the proposed estimators is studied via simulations. Entropy and extropy-based goodness-of-fit tests for uniformity are developed by the well performed estimators. The powers of the proposed uniformity tests are compared also via simulations assuming various alternatives and censoring schemes.