Stochastic Properties of Fractional Generalized Cumulative Residual Entropy and Its Extensions

Alomani, Ghadah; Kayid, Mohamed

doi:10.3390/e24081041

Cited by 4 publications

(4 citation statements)

References 24 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The present paper establishes some properties of

for coherent and mixed systems with lifetime T in situations where the component lifetimes are affected by each other and, furthermore, they are identically distributed. We recall that related results about the FCRE (as a special case of the FGCRE) can be seen in Alomani and Kayid [ 10 ], Kayid and Shrahili [ 11 ], and Xiong et al [ 12 ]. The main theoretical properties of this paper are associated with the general properties of the FGCRE, which allows suitably extending the CRE function.…”

Section: Introductionmentioning

confidence: 91%

“…From Corollary 1 of Alomani and Kayid [ 10 ], the FGCRE can be written based on the following covariance representation:

…”

Section: General Properties Of Fgcrementioning

confidence: 99%

“…Therefore, from Theorem 3 of Alomani and Kayid [ 10 ], we have

for all

Let

be the quantile function of S . If

, one can write the FGCRE as

where

Some examples of the FGCRE and the standard deviation of

are given in Table 1 .…”

Section: General Properties Of Fgcrementioning

confidence: 99%

See 2 more Smart Citations

Fractional Survival Functional Entropy of Engineering Systems

Alomani

Kayid

2022

Entropy

Self Cite

View full text Add to dashboard Cite

An alternate measure of uncertainty, termed the fractional generalized cumulative residual entropy, has been introduced in the literature. In this paper, we first investigate some variability properties this measure has and then establish its connection to other dispersion measures. Moreover, we prove under sufficient conditions that this measure preserves the location-independent riskier order. We then elaborate on the fractional survival functional entropy of coherent and mixed systems’ lifetime in the case that the component lifetimes are dependent and they have identical distributions. Finally, we give some bounds and illustrate the usefulness of the given bounds.

show abstract

“…The present paper establishes some properties of

Section: Introductionmentioning

confidence: 91%

“…From Corollary 1 of Alomani and Kayid [ 10 ], the FGCRE can be written based on the following covariance representation:

…”

Section: General Properties Of Fgcrementioning

confidence: 99%

See 1 more Smart Citation

Fractional Survival Functional Entropy of Engineering Systems

Alomani

Kayid

2022

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…The error displays a large tail when the elevation is minor. Due to the overbounding cumulative distribution function (CDF) [26] necessitating the location parameter 𝜇 is zero while the dual-component GMM REDM is recognized and specified in (4).…”

Section: Single-frequency Redm Formationmentioning

confidence: 99%

Overbounding Ifree errors based on bayesian Gaussian mixture model for ground-based augmentation system

Banu,

Shanavas

2024

IJECE

View full text Add to dashboard Cite

A dual-frequency measurement is employed in conjunction with an innovative Ifree filtering technique for mitigating the primary sources of Ifree influence on ground-based augmentation systems (GBAS) to safeguard the reliability of GBAS. The protective level achieved through the conventional Gaussian overbounding approach that are considered as much conventional technique. This adherence to tradition results in decreased reliability and a higher likelihood of false alarms. In contrast, the utilization of the Ifree algorithm contributes to reducing errors associated with dual-frequency measurements. This paper proposes the overbounding process according to Bayesian Gaussian mixture model (GMM) for maintaining Ifree-based GBAS range error. The Bayesian GMM is utilized for single-frequency model errors to examine the ambiguity estimations. The Monte Carlo (MC) simulation is established for defining estimated GMM assurance level accuracy which is attained through the general estimation method. Then, the last Bayesian GMM which is utilized for overbounding Ifree error distribution is investigated. According to the property of convolution invariance, the vertical protection in position field is determined without presenting difficult numerical calculations.

show abstract

Weighted survival functional entropy and its properties

Alomani

Kayid

2023

Open Physics

View full text Add to dashboard Cite

The weighted generalized cumulative residual entropy is a recently defined dispersion measure. This article introduces a new uncertainty measure as a generalization of the weighted generalized cumulative residual entropy, called it the weighted fractional generalized cumulative residual entropy of a nonnegative absolutely continuous random variable, which equates to the weighted fractional Shannon entropy. Several stochastic analyses and connections of this new measure to some famous stochastic orders are presented. As an application, we demonstrate this measure in random minima. The new measure can be used to study the coherent and mixed systems, risk measure, and image processing.

show abstract

Stochastic Properties of Fractional Generalized Cumulative Residual Entropy and Its Extensions

Cited by 4 publications

References 24 publications

Fractional Survival Functional Entropy of Engineering Systems

Fractional Survival Functional Entropy of Engineering Systems

Overbounding Ifree errors based on bayesian Gaussian mixture model for ground-based augmentation system

Weighted survival functional entropy and its properties

Contact Info

Product

Resources

About