The use of the Pareto distribution as a model for various socio-economic phenomena dates back to the late nineteenth century. In this paper, after some necessary preliminary results we deal with Bayes estimation of some of the parameters of interest under an asymmetric LINEX loss function, using suitable choice of priors when the scale parameter is known and unknown. Results of a Monte C...

We propose a unified framework to study policy evaluation (PE) and the associated temporal difference (TD) methods for reinforcement learning in continuous time space. show that PE is equivalent maintaining martingale condition of process. From this perspective, we find mean--square TD error approximates quadratic variation thus not suitable objective PE. present two use characterization design...

We describe a unifying method for proving relative loss bounds for online linear threshold classification algorithms, such as the Perceptron and the Winnow algorithms. For classification problems the discrete loss is used, i.e., the total number of prediction mistakes. We introduce a continuous loss function, called the “linear hinge loss”, that can be employed to derive the updates of the algo...

Stock market forecasting has attracted so many researchers and investors that ‎many studies have been done in this field. These studies have led to the ‎development of many predictive methods, the most widely used of which are ‎machine learning-based methods. In machine learning-based methods, loss ‎function has a key role in determining the model weights. In this study a new loss ‎function is ...

Recent results have demonstrated the ability of deep neural networks to serve as effective controllers (or function approximators of the value function) for complex sequential decision-making tasks, including those with raw visual inputs. However, to the best of our knowledge, such demonstrations have been limited to tasks either fully discrete or fully continuous actions. This paper introduces...

a 1993 result of j. llibre, and m. misiurewicz, (theorem a [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. also a 1980 result of l.s. block, j. guckenheimer, m. misiurewicz and l.s. young (lemma 1.5 [3]) states that if g is an a-graph of f then h(g) ? h( f ). in this pap...

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

This article studies the valuation of options written on the average level of a Markov process. The general properties of such options are examined. We propose a closed-form characterization in which the option payo is contingent on cumulative catastrophe losses. In our framework, the loss rate is a mean-reverting Markov process, with no continuous martingale component. The model supposes that ...