Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data

Nagy, Heba F.; Al-Omari, Amer Ibrahim; Hassan, Amal S.; Alomani, Ghadah

doi:10.3390/math10214102

Cited by 15 publications

(9 citation statements)

References 25 publications

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“…which implies that we can know the posterior distribution for each unknown parameter, with S Θ being the support of Θ , recalling that Θ = (w 1 , w 2 , w 3 , α, β) . The inclusion of the S-step of the SEM algorithm may be considered a Bayesian extension of the usual EM algorithm, as it consists of simulating U, W, and Θ from their posterior distributions, as indicated in (5). As described below, the simulation techniques we use here are the Gibbs sampling and Metropolis-Hastings algorithm [63].…”

Section: S-stepmentioning

confidence: 99%

“…Later, in [2], it was renamed the Kumaraswamy distribution. Additional references to this and related distributions include [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Recently, the trapezoidal Kumaraswamy (TK) distribution [17] was developed to enhance the flexibility of the Kumaraswamy distribution while preserving its fundamental properties.…”

Section: Introductionmentioning

confidence: 99%

“…Values of the mean DIC, EAIC, and EBIC in the indicated distribution for 100 samples of size 1000 generated from a Kumaraswamy distribution with parameters(5,10).…”

mentioning

confidence: 99%

“…Estimated posterior medians and means for 100 samples of size 1000 drawn from a Kumaraswamy distribution with parameters(5,10).…”

mentioning

confidence: 99%

See 3 more Smart Citations

Inference Based on the Stochastic Expectation Maximization Algorithm in a Kumaraswamy Model with an Application to COVID-19 Cases in Chile

et al. 2023

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Extensive research has been conducted on models that utilize the Kumaraswamy distribution to describe continuous variables with bounded support. In this study, we examine the trapezoidal Kumaraswamy model. Our objective is to propose a parameter estimation method for this model using the stochastic expectation maximization algorithm, which effectively tackles the challenges commonly encountered in the traditional expectation maximization algorithm. We then apply our results to the modeling of daily COVID-19 cases in Chile.

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Section: S-stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Inference Based on the Stochastic Expectation Maximization Algorithm in a Kumaraswamy Model with an Application to COVID-19 Cases in Chile

et al. 2023

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“…For more research on RSS-based reliability estimate [19,20,21,22,23]. Further findings on RSS-based parametric estimation encompass several estimation techniques [24,25,26,27,28,29]. Probability distribution models are essential and widely utilized in many domains, including physics, medicine, business management, engineering, etc.…”

Section: Introductionmentioning

confidence: 99%

Optimal Estimation of Power Chris-Jerry DistributionParameters Using Ranked Set Sampling Design withApplication

Alsadat,

Hassan,

Elgarhy

et al. 2024

Preprint

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Effective sample design has a major role in the quality of parameter estimation in statisticalparameter estimation issues. The ranking set sampling (RSS) strategy is effective and a less costlyoption than simple random sampling (SRS). A novel mixture continuous lifetime distribution thathas been proposed recently is the power Chris-Jerry distribution (PC-JD). It is useful for modelinga number of real data sets. This paper investigates the RSS approach for estimating the PC-JD’sparameters. There are roughly sixteen different techniques of estimation that are used, such as themaximum likelihood method, the percentiles method, some methods based on minimum distance,the Kolmogorov method, and some methods based on minimum and maximum spacing distances. Incomparison to a SRS, the simulation research assesses the performance of the suggested RSS-basedestimates in terms of some measures of accuracy. To identify the optimal estimating strategy, thepartial and overall ranks of many estimates are shown. According to numerical results, the maximumlikelihood approach seems to be quite beneficial in evaluating the estimated quality of RSS and SRS.RSS is a more effective sampling approach than SRS owing to its better efficiency. Additionally, thedifferent estimation techniques with survival data for both sampling techniques are examined

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On Estimating Multi- Stress Strength Reliability for Inverted Kumaraswamy Under Ranked Set Sampling with Application in Engineering

Hassan,

Alsadat,

Elgarhy

et al. 2024

J Nonlinear Math Phys

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The terrible operating constraints of many real-world events cause systems to malfunction regularly. The failure of systems to perform their intended duties when they reach their lowest, highest, or both extreme operating conditions is a phenomenon that researchers rarely focus on. The multi-stress strength reliability $$R = P(W<X<Z)$$ R = P ( W < X < Z ) is deemed in this study for a component whose strength X falls between two stresses, W, and Z, where X, W, and Z are independently inverted Kumaraswamy distributed. Both maximum likelihood and maximum product spacing procedures are employed to obtain the reliability estimator under simple random sampling (SRS) and ranked set sampling (RSS) methodologies. Four scenarios for reliability estimators are considered. The reliability estimator in the first and second cases can be determined by applying the same sample design (RSS/SRS) to the strength and stress distributions. When the sample data for W and Z originate from RSS while those for X are acquired from SRS, the third reliability estimator is calculated. The drawn data of the strength and stress random variables, which are obtained from SRS and RSS, respectively, are taken into consideration in the final scenario. The effectiveness of the suggested estimators is compared using a comprehensive computer simulation. Lastly, three real data sets have been used to determine reliability estimators.

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Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data

Cited by 15 publications

References 25 publications

Inference Based on the Stochastic Expectation Maximization Algorithm in a Kumaraswamy Model with an Application to COVID-19 Cases in Chile

Inference Based on the Stochastic Expectation Maximization Algorithm in a Kumaraswamy Model with an Application to COVID-19 Cases in Chile

Optimal Estimation of Power Chris-Jerry DistributionParameters Using Ranked Set Sampling Design withApplication

On Estimating Multi- Stress Strength Reliability for Inverted Kumaraswamy Under Ranked Set Sampling with Application in Engineering

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