Measure Of Inaccuracy Research Articles

Residual Inaccuracy Extropy and its properties

Abstract In this paper, we introduce a novel concept of a dynamic residual inaccuracy measure based on extropy. We extend the traditional residual inaccuracy measure to its dynamic version, which allows us to measure the discrepancy between two residual life distributions. We study the properties of the proposed measure, including its discrimination principle and the proportional hazard rate model. We also investigate a characterization problem related to the extropy inaccuracy measure and propose some alternative expressions of the dynamic residual measure of inaccuracy. Furthermore, we establish upper and lower bounds and some inequalities concerning dynamic residual inaccuracy measures based on extropy. We demonstrate that the defined measure of inaccuracy is invariant under scale but not under location transformation. The given findings have important implications for statistical inference, estimation, and modeling. The proposed extropy-based dynamic residual inaccuracy measure provides a powerful tool for quantifying the discrepancy between two residual life distributions over time. At the end of the paper, we provide two non-parametric estimators for the proposed extropy measure of inaccuracy for both the non-censored (complete sample) and the right-censored scheme. The performances of these estimators are compared numerically based on their bias and MSE.

Extended weighted generalized cumulative residual entropy for risk measurement

In this paper, we propose an extended variant of Weighted Generalized Cumulative Residual Entropy (WGCRE), its dynamic version, and a Weighted Generalized Cumulative Kerridge Inaccuracy measure by considering a general continuous non negative weight function. Several properties, including bounds and stochastic ordering, of these measures are obtained under appropriate assumptions. Furthermore, we introduce the empirical extended WGCRE as a non-parametric estimator, demonstrating its almost sure convergence to the proposed measure. A central limit theorem is established, examples are provided for illustrative purposes, and the stability of the empirical measure is examined. Finally, we demonstrate the practicality of this measure using real financial data for risk measurement.

Residual and past varinaccuracy measures

Abstract Analysing the information measures’ dispersion index has garnered increasing attention. In this regard, variability of entropy has been explored for residual and past lifetimes. In a recent paper, Balakrishnan et al. (2023, Commun. Stat. Theory Methods, 53, 5574–5592) have studied the variability of the Kerridge inaccuracy measure. The dynamic measures of varinaccuracy, namely residual varinaccuracy and past varinaccuracy, have been introduced in this article. A detailed course of theoretical results has been investigated with examples. Further, some applications of the residual varinaccuracy have been added to show the functionality of the defined measure.

On weighted version of dynamic cumulative residual inaccuracy measure based on extropy

On weighted version of dynamic cumulative residual inaccuracy measure based on extropy

Safety enhancement for nonlinear systems via learning-based model predictive control with Gaussian process regression

This paper proposes a novel safe Gaussian process model predictive control scheme for discrete-time nonlinear systems subject to additive uncertainties. The scheme is implemented using an online learning framework that provides safety guarantees based on a nominal model, and employs Gaussian process regression (GPR) to learn the uncertainties to improve the control performance. The advantage of this framework lies in the ability to decouple safety and performance in the robust controller design. Furthermore, the inaccuracy measure given by GPR can be used to adaptively tighten the constraints, leading to the less conservative behaviors. A rigorous analysis of the constraint satisfaction, recursive feasibility and closed-loop stability is also presented. Two simulation examples, including a regulation problem of a nominally linear system and a tracking problem of a car whose model is nonlinear, are performed to verify the effectiveness of the proposed scheme.

On the dynamic residual measure of inaccuracy based on extropy in order statistics

AbstractIn this paper, we introduce a novel way to quantify the remaining inaccuracy of order statistics by utilizing the concept of extropy. We explore various properties and characteristics of this new measure. Additionally, we expand the notion of inaccuracy for ordered random variables to a dynamic version and demonstrate that this dynamic information measure provides a unique determination of the distribution function. Moreover, we investigate specific lifetime distributions by analyzing the residual inaccuracy of the first-order statistics. Nonparametric kernel estimation of the proposed measure is suggested. Simulation results show that the kernel estimator with bandwidth selection using the cross-validation method has the best performance. Finally, an application of the proposed measure on the model selection is provided.

Optimal recovery of the derivate from the confined analytic function

In the article the author finds out the best straight-line method to recover the derivate in zero-point from the confined analytic function determined in the unit circle according to values of the function and values of its derivate in given points creating the regular polygon with zero as the center. The paper consists of three parts. The first part one contains notions and results necessary for the solution of the objective. The second part determines the measure of inaccuracy of the best approximation method and draws out the corresponding extremum function. It is established that the extremum function is the only one to an approximation of the constant multiplier modulo equal to one. The third part calculates coefficients of the best straight-line method of recovery. It is established that the best straight- linear method of recovery is the only one.

A new two-parametric weighted generalized inaccuracy measure

Abstract In this article, we present a novel approach to measuring inaccuracy, introducing a two-parametric weighted generalized inaccuracy measure of order α and type β, along with its residual version. Our proposed measure depends on the proportional hazard rate model (PHRM) to uniquely determine the survival function, and we have derived a characterization result for this measure. Through our analysis under the PHRM framework, we have studied various properties of the proposed measure and their interrelationships.

Extropy based inaccuracy measure in order statistics

In this paper, we provide a measure based on inaccuracy between distributions of the ith order statistic and the parent random variable. This measure characterizes the distribution function of parent random variable uniquely. We demonstrate that the extropy of the parent random variable is the average of the accuracy measure. It is also shown that the measure of inaccuracy defined is invariant under scale but not under location transformation. Nonparametric estimators for the proposed measures are also obtained. A Monte Carlo simulation study is performed to verify the performance of the suggested estimators. Simulation results show that the estimator based on the reflection boundary technique for probability density function estimation and the empirical method for cumulative distribution function estimation has the best performance among estimators. Also, a real dataset is considered to show an application of the proposed estimators on model selection.

An inaccuracy measure between non-explosive point processes with applications to Markov chains

AbstractInaccuracy and information measures based on cumulative residual entropy are quite useful and have received considerable attention in many fields, such as statistics, probability, and reliability theory. In particular, many authors have studied cumulative residual inaccuracy between coherent systems based on system lifetimes. In a previous paper (Bueno and Balakrishnan, Prob. Eng. Inf. Sci.36, 2022), we discussed a cumulative residual inaccuracy measure for coherent systems at component level, that is, based on the common, stochastically dependent component lifetimes observed under a non-homogeneous Poisson process. In this paper, using a point process martingale approach, we extend this concept to a cumulative residual inaccuracy measure between non-explosive point processes and then specialize the results to Markov occurrence times. If the processes satisfy the proportional risk hazard process property, then the measure determines the Markov chain uniquely. Several examples are presented, including birth-and-death processes and pure birth process, and then the results are applied to coherent systems at component level subject to Markov failure and repair processes.

A scoring rule and global inaccuracy measure for contingent varying importance

Levinstein recently presented a challenge to accuracy-first epistemology. He claims that there is no strictly proper, truth-directed, additive, and differentiable scoring rule that recognises the contingency of varying importance, i.e., the fact that an agent might value the inaccuracy of her credences differently at different possible worlds. In my response, I will argue that accuracy-first epistemology can capture the contingency of varying importance while maintaining its commitment to additivity, propriety, truth-directedness, and differentiability. I will construct a scoring rule — a weighted scoring rule — and a global inaccuracy measure that has all four required properties and recognises the contingency of varying importance. I will show that Levinstein’s and my results coexist without contradicting each other

Some Generalizations Concerning Inaccuracy Measures

Some Generalizations Concerning Inaccuracy Measures

Dispersion indices based on Kerridge inaccuracy measure and Kullback-Leibler divergence

Recently, a new dispersion index, as a measures of information, has been introduced and called varentropy. In this article, we introduce new measures of variability based on two measures of uncertainty, namely, the Kerridge inaccuracy measure and the Kullback-Leibler divergence. Their generating functions are considered and their infinite series representations are given. These new measures and associated properties, bounds and illustrative examples are all presented in detail. Finally, an application of Kullback-Leibler divergence and its dispersion index is illustrated by using the mean-variance rule.

A Note on Verisimilitude and Accuracy

M. Schoenfield has constructed examples of proper inaccuracy measures that value verisimilitude (in a certain sense) in spaces of worlds equipped with a particular variety of verisimilitude metric. However, Schoenfield left it as an open question whether `for every space of worlds, there is a proper inaccuracy measure that values verisimilitude.' Here we answer this question in the affirmative.

A new measure of inaccuracy for record statistics based on extropy

AbstractWe introduce a new measure of inaccuracy based on extropy between distributions of the nth upper (lower) record value and parent random variable and discuss some properties of it. A characterization problem for the proposed extropy inaccuracy measure has been studied. It is also shown that the defined measure of inaccuracy is invariant under scale but not under location transformation. We characterize certain specific lifetime distribution functions. Nonparametric estimators based on the empirical and kernel methods for the proposed measures are also obtained. The performance of estimators is also discussed using a real dataset.

Jensen–Inaccuracy Information Measure

The purpose of the paper is to introduce the Jensen-inaccuracy measure and examine its properties. Furthermore, some results on the connections between the inaccuracy and Jensen-inaccuracy measures and some other well-known information measures are provided. Moreover, in three different optimization problems, the arithmetic mixture distribution provides optimal information based on the inaccuracy information measure. Finally, two real examples from image processing are studied and some numerical results in terms of the inaccuracy and Jensen-inaccuracy information measures are obtained.

Results and applications of a new inaccuracy measure based on cumulative Tsallis entropy

Non-additive measures are important for many applications. In this paper we propose an extension of the non-additive measure using the concept of Kerridge inaccuracy and cumulative Tsallis entropy. Several properties including non-linear transformation, bounds and characterizations are obtained using this measure. We also study different properties of the quantile version of the proposed measure. Finally, we numerically illustrate the usefulness of the measure and its quantile form using kernel density estimators.

Comparison between the two Huang-Kotz FGM types by some information measures in generalized order statistics and their concomitants

In this paper, we study the concomitants of m?dual generalized order statistics (and consequently m?generalized order statistics) from Huang-Kotz Farlie-Gumble-Morgenstern bivariate distribution (HK-FGM) of the types 1 and 2. Some important information measures are derived and studied for ordinary order statistics and sequential order statistics with a comparison. Specifically, the Shannon entropy, inaccuracy measure, and Fisher information number. Moreover, a comparison between the two types of HK-FGM distribution is carried out.

Information Measures and Concomitants of k-Record Values Based on Sarmanov Family of Bivariate Distributions

In this paper, the marginal distributions of concomitants of k-record values based on Sarmanov family of bivariate distributions are obtained, as an extension of several recent papers. Besides, we derive the joint distribution of concomitants of k-record values for this family. Furthermore, some new and useful properties of information measures, namely, the extropy, Shannon entropy, inaccuracy measure, cumulative entropy, cumulative residual entropy, and cumulative residual Fisher information are studied. Finally, we offered various examples accompanied by numerical investigations that backed up the theoretical findings.

On dynamic cumulative past inaccuracy measure based on extropy

An alternate measure of extropy based on the cumulative distribution function rather than the probability density function of a random variable is called the cumulative past extropy (CPE). In this communication, the concept of CPE has been extended to cumulative past extropy inaccuracy (CPEI) and then to a dynamic version of it. A characterization problem for the proposed dynamic extropy inaccuracy measure has been studied under the proportional reversed hazard rate model. We also discuss the stochastic ordering of dynamic cumulative past extropy and certain results based on it. Some well-known lifetime distributions have been characterized using the proposed dynamic cumulative past extropy inaccuracy (DCPEI) measure. Three methods for nonparametric estimation of the DCPEI measure based on kernel and empirical estimators are proposed. Simulation results show that the kernel-based estimators of the DCPEI measure perform better than the empirical-based estimator under different sample sizes and times. A real data set is considered to show the behavior of the estimators in real cases.