Mixture Representations of the Extropy of Conditional Mixed Systems and Their Information Properties

Pakdaman, Zohreh; Hashempour‎, Majid

doi:10.1007/s40995-021-01121-4

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…Also, estimates obtained by using different kernels are usually numerically very similar. So, the choice of kernel K is not too important and the standard normal density function is used as the kernel function K (•) in Equation (22). What does matter much more is the choice of bandwidth which controls the amount of smoothing.…”

Section: Nonparametric Estimationmentioning

confidence: 99%

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

Mohammadi,

Hashempour,

Kamari

2024

Prob. Eng. Inf. Sci.

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In 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.

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Section: Nonparametric Estimationmentioning

confidence: 99%

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

Mohammadi,

Hashempour,

Kamari

2024

Prob. Eng. Inf. Sci.

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“…Yang et al [32] studied the relations between extropy and variational distance and determined the distribution that attains the minimum or maximum extropy among these distributions within a given variation distance from any given probability distribution. Also, for more details, see [19,20] and references therein. Jahanshahi et al [11] introduced an alternative measure of uncertainty of nonnegative random variable X, which they called the cumulative residual extropy (CRJ), given as…”

Section: Extropymentioning

confidence: 99%

A new measure of inaccuracy for record statistics based on extropy

Hashempour‎

Mohammadi

2023

Prob. Eng. Inf. Sci.

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We 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.

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Extropy based inaccuracy measure in order statistics

Mohammadi,

Hashempour

2023

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Mixture Representations of the Extropy of Conditional Mixed Systems and Their Information Properties

Cited by 3 publications

References 20 publications

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

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

A new measure of inaccuracy for record statistics based on extropy

Extropy based inaccuracy measure in order statistics

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