Quantile Version of Mathai-Haubold Entropy of Order Statistics

Almanjahie, Ibrahim M.; Dar, Javid Gani; Al-Omari, Amer Ibrahim; Aijaz, Mir

doi:10.32604/cmes.2021.014896

Cited by 3 publications

(3 citation statements)

References 20 publications

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“…It can be defined as the average number of sample points plotted on the control chart before the control chart shows an OOC signal [41]. Mathematically it is defined as ARL = N i=1 RL i /N, where N is the size of simulation runs (see Almanjahie et al [42]). For the IC process, the control chart should have large ARL 0 to avoid the false alarm, while for the OOC process the ARL 1 should be small for early shifts detection.…”

Section: Performance Evaluationmentioning

confidence: 99%

Ranked-Set Sampling Based Distribution Free Control Chart with Application in CSTR Process

Almanjahie¹,

Rasheed²,

Khan³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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Nonparametric (distribution-free) control charts have been introduced in recent years when quality characteristics do not follow a specific distribution. When the sample selection is prohibitively expensive, we prefer ranked-set sampling over simple random sampling because ranked set sampling-based control charts outperform simple random sampling-based control charts. In this study, we proposed a nonparametric homogeneously weighted moving average based on the Wilcoxon signed-rank test with ranked set sampling (NPHWMA RSS ) control chart for detecting shifts in the process location of a continuous and symmetric distribution. Monte Carlo simulations are used to obtain the run length characteristics to evaluate the performance of the proposed NPHWMA RSS control chart. The proposed NPHWMA RSS control chart's performance is compared to that of parametric and nonparametric control charts. These control charts include the exponentially weighted moving average (EWMA) control chart, Wilcoxon signed-rank with simple random sampling based the nonparametric EWMA control chart, the nonparametric EWMA sign control chart, Wilcoxon signed-rank with ranked set sampling-based the nonparametric EWMA control chart, and the homogeneously weighted moving average control charts. The findings show that the proposed NPHWMA RSS control chart performs better than its competitors, particularly for the small shifts. Finally, an example is presented to demonstrate how the proposed scheme can be implemented practically.

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Section: Performance Evaluationmentioning

confidence: 99%

Ranked-Set Sampling Based Distribution Free Control Chart with Application in CSTR Process

Almanjahie¹,

Rasheed²,

Khan³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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“…Several works have focused on the derivation of these measures for specific distributions [31][32][33]. These measures are derived for one of the proposed families in what follows.…”

Section: Entropymentioning

confidence: 99%

“…Additionally, if we use the binomial expansion of the last equation and insert it in the equation above related to the expansion of power series in (33), we have the follow expression:…”

Section: Rényi Entropymentioning

confidence: 99%

An Extended log-Lindley-G Family: Properties and Experiments in Repairable Data

2021

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In this article, two new families of distributions are proposed: the generalized log-Lindley-G (GLL-G) and its counterpart, the GLL*-G. These families can be justified by their relation to the log-Lindley model, an important assumption for describing social and economic phenomena. Specific GLL models are introduced and studied. We show that the GLL density is rewritten as a two-member linear combination of the exponentiated G-densities and that, consequently, many of its mathematical properties arise directly, such as moment-based expressions. A maximum likelihood estimation procedure for the GLL parameters is provided and the behavior of the resulting estimates is evaluated by Monte Carlo experiments. An application to repairable data is made. The results argue for the use of the exponential law as the basis for the GLL-G family.

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Unit compound Rayleigh model: Statistical characteristics, estimation and application

Gong,

Luo,

Ren

2024

MATH

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<p>In this paper, we proposed a novel probability distribution model known as the unit compound Rayleigh distribution, which possesses the distinctive characteristic of defining the range within the bounded interval (0, 1). Through an in-depth investigation of this distribution, we analyzed various statistical and structural characteristics including reliability function, risk function, quantile function, moment analysis, order statistics, and entropy measurement. To estimate the unknown parameters of our proposed distribution model, we employed maximum likelihood (ML) estimation and Bayesian estimation. Furthermore, we derived several entropy measures based on ML estimation under the unit compound Rayleigh distribution. To comprehensively evaluate the performance of these entropies, we employed the Monte Carlo simulation method to calculate the average entropy estimate, average entropy bias, corresponding mean square error, and mean relative estimate for assessing the performance of various entropies within the unit compound Rayleigh distribution model. Finally, in order to validate its potential for practical applications, two sets of real data were selected for empirical analysis where fitting and parameter estimation were conducted to demonstrate the advantages of utilizing the unit compound Rayleigh distribution in describing and predicting actual data. This study not only introduces a new probability theory and statistics framework by proposing a novel distribution model but also provides researchers and practitioners in related fields with a powerful analytical tool.</p>

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Quantile Version of Mathai-Haubold Entropy of Order Statistics

Cited by 3 publications

References 20 publications

Ranked-Set Sampling Based Distribution Free Control Chart with Application in CSTR Process

Ranked-Set Sampling Based Distribution Free Control Chart with Application in CSTR Process

An Extended log-Lindley-G Family: Properties and Experiments in Repairable Data

Unit compound Rayleigh model: Statistical characteristics, estimation and application

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