Weighted extensions of generalized cumulative residual entropy and their applications

Tahmasebi, Saeid

doi:10.1080/03610926.2019.1615094

Cited by 10 publications

(21 citation statements)

References 23 publications

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“…By substituting z = t and y = x − t, x ≥ t, we obtain ψ(x) − ψ(t) ≥ (≤) ψ(x − t) for all x, t ≥ 0. Recalling (7), for t ≥ 0, we find that…”

Section: Variance Of a Transformed Random Variablementioning

confidence: 95%

“…to ensure the finiteness of m ψ (t). In particular, when ψ(t) = t, and hence φ(t) = 1, then (7) coincides with the MRL function (5).…”

Section: Variance Of a Transformed Random Variablementioning

confidence: 96%

“…Recently, the WCRE was extended in Tahmasebi [7] by the weighted generalized cumulative residual entropy (WGCRE) expressed as…”

Section: Introductionmentioning

confidence: 99%

“…In particular, by taking φ(x) ≡ 1 in (3), we immediately derive the generalized cumulative residual entropy (GCRE), see Psarrakos and Navarro [8]. Various characteristics of the generalized measure (3) and its connection with some other notions have been studied in Tahmasebi [7]. See Kayal [9] for some characterizations of weighted GCRE for the linear weight function φ(x) = x.…”

Section: Introductionmentioning

confidence: 99%

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Connections between Weighted Generalized Cumulative Residual Entropy and Variance

Toomaj

Crescenzo

2020

Mathematics

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A shift-dependent information measure is favorable to handle in some specific applied contexts such as mathematical neurobiology and survival analysis. For this reason, the weighted differential entropy has been introduced in the literature. In accordance with this measure, we propose the weighted generalized cumulative residual entropy as well. Despite existing apparent similarities between these measures, however, there are quite substantial and subtle differences between them because of their different metrics. In this paper, particularly, we show that the proposed measure is equivalent to the generalized cumulative residual entropy of the cumulative weighted random variable. Thus, we first provide expressions for the variance and the new measure in terms of the weighted mean residual life function and then elaborate on some characteristics of such measures, including equivalent expressions, stochastic comparisons, bounds, and connection with the excess wealth transform. Finally, we also illustrate some applications of interest in system reliability with reference to shock models and random minima.

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“…By substituting z = t and y = x − t, x ≥ t, we obtain ψ(x) − ψ(t) ≥ (≤) ψ(x − t) for all x, t ≥ 0. Recalling (7), for t ≥ 0, we find that…”

Section: Variance Of a Transformed Random Variablementioning

confidence: 95%

“…to ensure the finiteness of m ψ (t). In particular, when ψ(t) = t, and hence φ(t) = 1, then (7) coincides with the MRL function (5).…”

Section: Variance Of a Transformed Random Variablementioning

confidence: 96%

“…Recently, the WCRE was extended in Tahmasebi [7] by the weighted generalized cumulative residual entropy (WGCRE) expressed as…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Connections between Weighted Generalized Cumulative Residual Entropy and Variance

Toomaj

Crescenzo

2020

Mathematics

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“…The asymptotic distribution of this linear function of sample spacing can be found, for example in Di Crescenzo & Longobardi (2009) and Tahmasebi (2019) only for exponential and standard uniform distributions. So we provide another estimator for ξJ (X) which is a linear function of order statistics.…”

Section: A New Estimation 80mentioning

confidence: 99%

Cumulative Residual Extropy of Minimum Ranked Set Sampling with Unequal Samples

Kazemia¹,

Tahmasebib²,

Calì³

et al. 2020

Preprint

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Recently, an alternative measure of uncertainty called cumulative residual extropy (CREX) was proposed by Jahanshahi et al. (2019). In this paper, we consider uncertainty measures of minimum ranked set sampling procedure with unequal samples (MinRSSU) in terms of CREX and its dynamic version and we compare the uncertainty and information content of CREX based on MinRSSU and simple random sampling (SRS) designs. Also, using simulation, we study on new estimators of CREX for MinRSSU and SRS designs in terms of bias and mean square error. Finally, we provide a new discrimination measure of disparity between the distribution of MinRSSU and parental data SRS.

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Some properties of weighted survival extropy and its extended measures

Chakraborty

Pradhan

2022

Communications in Statistics - Theory and Methods

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Weighted extensions of generalized cumulative residual entropy and their applications

Cited by 10 publications

References 23 publications

Connections between Weighted Generalized Cumulative Residual Entropy and Variance

Connections between Weighted Generalized Cumulative Residual Entropy and Variance

Cumulative Residual Extropy of Minimum Ranked Set Sampling with Unequal Samples

Some properties of weighted survival extropy and its extended measures

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