This paper focuses on two main issues that are based on two important concepts: exponential Levy process and minimal entropy martingale measure. First, we intend to obtain   risk measurement such as value-at-risk (VaR) and conditional value-at-risk (CvaR) using Monte-Carlo methodunder minimal entropy martingale measure (MEMM) for exponential Levy process. This Martingale measure is used for the...

An extension of the entropy power inequality to the form N r (X +Y ) ≥ N r (X) +N r (Y ) with arbitrary independent summands X and Y in R is obtained for the Rényi entropy and powers α ≥ (r + 1)/2.

We introduce a new family of continuous models called the beta odd log-logistic generalized family of distributions. We study some of its mathematical properties. Its density function can be symmetrical, left-skewed, right-skewed, reversed-J, unimodal and bimodal shaped, and has constant, increasing, decreasing, upside-down bathtub and J-shaped hazard rates. Five special models are discussed. W...

It is often stated in papers tackling the task of selecting a Bayesian network structure from data that there are these two distinct approaches: (i) Apply conditional indepen­ dence tests . when testing for the presence or otherwise of edges; (ii) Search the model space using a scoring metric. Here I argue that for complete data and a given node ordering this division is largely a myth, by show...

The notion of smooth entropy allows a unifying, generalized formulation of privacy ampli-cation and entropy smoothing. Smooth entropy is a measure for the number of almost uniform random bits that can be extracted from a random source by probabilistic algorithms. It is known that the R enyi entropy of order at least 2 of a random variable is a lower bound for its smooth entropy. On the other ha...

As a novel data mining approach, a wavelet entropy algorithm is used to perform entropy statistics on wavelet coefficients (or reconstructed signals) at various wavelet scales on the basis of wavelet decomposition and entropy statistic theory. Shannon wavelet energy entropy, one kind of wavelet entropy algorithm, has been taken into consideration and utilized in many areas since it came into be...

in this paper, we derive the exact analytical expressions for the shannon entropy of generalized orderstatistics from pareto-type and related distributions.

Probability representation entropy (tomographic entropy) of arbitrary quantum state is introduced. Using the properties of spin tomogram to be standard probability distribution function the tomographic entropy notion is discussed. Relation of the tomographic entropy to Shannon entropy and von Neumann entropy is elucidated.

Di Crescenzo and Longobardi (2002) has been proposed a measure of uncertainty related to past life namely past entropy. The present paper addresses the question of extending this concept to bivariate set-up and study some properties of the proposed measure. It is shown that the proposed measure uniquely determines the distribution function. Characterizations for some bivariate lifetime models a...