6 research outputs found
Weighted cumulative residual Entropy Generating Function and its properties
The study on the generating function approach to entropy become popular as it
generates several well-known entropy measures discussed in the literature. In
this work, we define the weighted cumulative residual entropy generating
function (WCREGF) and study its properties. We then introduce the dynamic
weighted cumulative residual entropy generating function (DWCREGF). It is shown
that the DWCREGF determines the distribution uniquely. We study some
characterization results using the relationship between the DWCREGF and the
hazard rate and/or the mean residual life function. Using a characterization
based on DWCREGF, we develop a new goodness fit test for Rayleigh distribution.
A Monte Carlo simulation study is conducted to evaluate the proposed test.
Finally, the test is illustrated using two real data sets.Comment: arXiv admin note: text overlap with arXiv:2211.0548
Cumulative Information Generating Function and Generalized Gini Functions
We introduce and study the cumulative information generating function, which
provides a unifying mathematical tool suitable to deal with classical and
fractional entropies based on the cumulative distribution function and on the
survival function. Specifically, after establishing its main properties and
some bounds, we show that it is a variability measure itself that extends the
Gini mean semi-difference. We also provide (i) an extension of such a measure,
based on distortion functions, and (ii) a weighted version based on a mixture
distribution. Furthermore, we explore some connections with the reliability of
-out-of- systems and with stress-strength models for multi-component
systems. Also, we address the problem of extending the cumulative information
generating function to higher dimensions.Comment: 25 pages, 1 figure, submitted for publication on November 30, 202
What is the Fourier Transform of a Spatial Point Process?
This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions; first what is the natural definition of a Fourier transform, and what are its spectral moments, second we calculate fourth order moments of the Fourier transform using Campbell’s theorem. Third we determine how to implement tapering, an important component for spectral analysis of other stochastic processes. Fourth we answer the question of how to produce an isotropic representation of the Fourier transform of the process. This determines the basic spectral properties of an observed spatial point process
A precise bare simulation approach to the minimization of some distances. Foundations
In information theory -- as well as in the adjacent fields of statistics,
machine learning, artificial intelligence, signal processing and pattern
recognition -- many flexibilizations of the omnipresent Kullback-Leibler
information distance (relative entropy) and of the closely related Shannon
entropy have become frequently used tools. To tackle corresponding constrained
minimization (respectively maximization) problems by a newly developed
dimension-free bare (pure) simulation method, is the main goal of this paper.
Almost no assumptions (like convexity) on the set of constraints are needed,
within our discrete setup of arbitrary dimension, and our method is precise
(i.e., converges in the limit). As a side effect, we also derive an innovative
way of constructing new useful distances/divergences. To illustrate the core of
our approach, we present numerous examples. The potential for widespread
applicability is indicated, too; in particular, we deliver many recent
references for uses of the involved distances/divergences and entropies in
various different research fields (which may also serve as an interdisciplinary
interface)