Comparison of estimation methods for unit-Gamma distribution

Dey, Sanku; Menezes, F. B.; Mazucheli, Josmar

doi:10.6339/jds.201910_17(4).0009

Cited by 7 publications

(2 citation statements)

References 29 publications

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“…The data are measured in millions of cubic feet per second; see Table 5. Dumonceaux and Antle [24] presented this information, which was later assessed by Dey et al [25]. To highlight the superiority of the ULL lifetime model based on the full MFL data, we will compare it with seven other models in the literature, named:…”

Section: Environmental Data Analysismentioning

confidence: 99%

Estimation and Optimal Censoring Plan for a New Unit Log-Log Model via Improved Adaptive Progressively Censored Data

Alotaibi,

Nassar,

Elshahhat

2024

Axioms

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To gather enough data from studies that are ongoing for an extended duration, a newly improved adaptive Type-II progressive censoring technique has been offered to get around this difficulty and extend several well-known multi-stage censoring plans. This work, which takes this scheme into account, focuses on some conventional and Bayesian estimation missions for parameter and reliability indicators, where the unit log-log model acts as the base distribution. The point and interval estimations of the various parameters are looked at from a classical standpoint. In addition to the conventional approach, the Bayesian methodology is examined to derive credible intervals beside the Bayesian point by leveraging the squared error loss function and the Markov chain Monte Carlo technique. Under varied settings, a simulation study is carried out to distinguish between the standard and Bayesian estimates. To implement the proposed procedures, two actual data sets are analyzed. Finally, multiple precision standards are considered to pick the optimal progressive censoring scheme.

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Section: Environmental Data Analysismentioning

confidence: 99%

Estimation and Optimal Censoring Plan for a New Unit Log-Log Model via Improved Adaptive Progressively Censored Data

Alotaibi,

Nassar,

Elshahhat

2024

Axioms

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“…Later, Lima-Filho et al [6] constructed an inflated beta control chart. Apart from beta distribution, the unit gamma (UG) can exhibit constant, unimodal, increasing, and decreasing shapes, whereas its hazard function has bathtub and decreasing shapes [7]. Grassia [8] gave a detailed overview of this distribution as well as of its variants.…”

Section: Introductionmentioning

confidence: 99%

Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions

Akram

Ali

Shah

et al. 2022

Journal of Mathematics

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Quick detection of an assignable cause is necessary for process accuracy with respect to the specifications. The aim of this study is to monitor the time and magnitude processes based on unit-interval data. To this end, maximum exponentially weighted moving average (Max-EWMA) control chart for simultaneous monitoring time and magnitude of an event is proposed. To be precise, beta and unit gamma distributions are considered to develop the Max-EWMA chart. The chart’s performance is accessed using average run length (ARL), the standard deviation of run length (SDRL), and different quantiles of the run length distribution through extensive Monte Carlo simulations. Besides a comprehensive simulation study, the proposed charting methodology is applied to a real data set. The results show that the proposed chart is more efficient in detecting small to medium-sized shifts. The results also indicate that simultaneous shifts are detected more quickly as compared to the pure shift.

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Study of a bounded interval perks distribution with quantile regression analysis

Al‐Essa,

Shafiq,

Ozonur

et al. 2024

Statistical Analysis

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In this article, a novel bounded interval model called the unit‐Perks model is developed by suitably transforming the positive random variable of the Perks distribution. Numerous statistical features of the bounded interval Perks model are being explored based on the expansion of the density function. Eight distinct estimation approaches are being used to estimate the parameters of the unit‐Perks model. A throughout simulation analysis is also included to evaluate the precision of the resulting estimators from eight estimating approaches. Two real bounded interval data sets are being utilized to investigate the practical applicability of the unit‐Perks model. A comparison is also made to determine which method of estimation works better for the given model. According to a comparison of eight different estimation approaches, the maximum likelihood estimation approach outperformed than the other seven estimating approaches. The unit‐perks model is then used to introduce the quantile regression model named as quantile unit‐Perks distribution. Application to real data set for the quantile unit‐Perks distribution is also performed. The quantile residuals are used for the residual analysis of the fitted regression model. On the basis of mathematical, computational, and pictorial evidences, it is concluded that the presented model exhibited greater modeling capabilities.

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Comparison of estimation methods for unit-Gamma distribution

Cited by 7 publications

References 29 publications

Estimation and Optimal Censoring Plan for a New Unit Log-Log Model via Improved Adaptive Progressively Censored Data

Estimation and Optimal Censoring Plan for a New Unit Log-Log Model via Improved Adaptive Progressively Censored Data

Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions

Study of a bounded interval perks distribution with quantile regression analysis

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