A comprehensive toolbox for the gamma distribution: The gammadist package

Chen, Piao; Buis, K.; Zhao, Xiujie

doi:10.1080/00224065.2022.2053794

Cited by 9 publications

(3 citation statements)

References 35 publications

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“…(2021), Zhang et al . (2022) and Chen, Buis & Zhao (2023). The reader is referred to Hannig, Iyer & Patterson (2006) for a comprehensive introduction to FGPQs.…”

Section: Notation and Definitionsmentioning

confidence: 99%

“…FGPQs are often used to develop inference procedures for complicated functions of parameters in the presence of nuisance parameters. Recent applications include those by Wang et al (2021), Zhang et al (2022) and Chen, Buis & Zhao (2023). The reader is referred to Hannig, Iyer & Patterson (2006) for a comprehensive introduction to FGPQs.…”

Section: Fiducial Generalised Pivotal Quantitiesmentioning

confidence: 99%

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Testing multiple dispersion effects from unreplicated order‐of‐addition experiments

Tsai,

2024

Aus NZ J of Statistics

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SummaryOptimal addition orders of several components can be determined systematically to address order‐of‐addition problems when active location and dispersion effects are both taken into account. Based on the concept of fiducial generalised pivotal quantities, a new testing procedure is proposed in this paper to identify active dispersion effects from unreplicated order‐of‐addition experiments. Because the proposed method is free of all nuisance parameters indexed by the requirement set, it is capable of testing multiple dispersion effects. Simulation results show that the proposed method can maintain the empirical sizes close to the nominal level. A paint viscosity study is used to show that the proposed method can be practical. In addition, testable requirement sets are characterised when an order‐of‐addition orthogonal array is used to design an experiment.

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“…(2021), Zhang et al . (2022) and Chen, Buis & Zhao (2023). The reader is referred to Hannig, Iyer & Patterson (2006) for a comprehensive introduction to FGPQs.…”

Section: Notation and Definitionsmentioning

confidence: 99%

Section: Fiducial Generalised Pivotal Quantitiesmentioning

confidence: 99%

Testing multiple dispersion effects from unreplicated order‐of‐addition experiments

Tsai,

2024

Aus NZ J of Statistics

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“…It outperforms the Shewhart chart, as shown in parameter analysis and a real data case study. Chen et al 24 developed a comprehensive toolbox, known as the gammadist package, to enhance the analysis of the gamma distribution. Al-Omari and Dobbah 25 investigated the mixture of Shanker and gamma distributions and its relevance to engineering data.…”

Section: Introductionmentioning

confidence: 99%

Symmetry of gamma distribution data about the mean after processing with EWMA function

Hamasha,

Obeidat,

Alzoubi

et al. 2023

Sci Rep

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Statistical Process Control (SPC) plays a vital role in maintaining quality and reducing variability in manufacturing processes. Among SPC techniques, the Exponentially Weighted Moving Average (EWMA) stands out for its ability to detect small process shifts quickly, making it a valuable tool in ensuring product consistency and preventing quality issues. EWMA constructs control charts to monitor process mean shifts, tracks product/service quality by identifying variations, and monitors manufacturing process parameters for early detection of deviations and necessary adjustments. EWMA control chart has been proposed as an alternative to the Shewhart control chart. Sequential measurements are processed using the EWMA function before being placed on the control chart. One of the crucial concerns about the EWMA control chart is the asymmetry of the data around the mean. Although processing with the EWMA function reduces data skewness, the problem of asymmetric data may not be solved. The control chart is designed to leave in front of the upper control limit (UCL) α/2 of the data and behind the lower control limit (LCL) another α/2 of the data, and this does not occur in the case of symmetric data. α/2 represents the significance level for each tail in a two-tailed hypothesis test, indicating the probability of incorrectly rejecting the null hypothesis for each side of the distribution. Since many of the distributions in real life can be approximated by the Gamma distribution, the Gamma distribution was adopted in this study. The Monte Carlo simulation methodology was implemented to generate Gamma distributed data, process it with EWMA function and assess the skewness and kurtosis. The purpose of this paper is to evaluate the effect of EWMA parameters on the performance of the EWMA control chart. Moreover, it focuses on skewness and kurtosis reduction after data processing using the EWMA function. The findings help researchers and practitioners to select the best parameters. Further, the research investigates the effect of EWMA parameter on the shape of distribution.

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Performance Analysis of Free Space Optical System Over Inverse Gaussian Gamma Turbulence Channel

Rani,

Jayanthi,

Mandpura

2024

Trans Emerging Tel Tech

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Free space optical (FSO) communication is a proficient technology with potential applications in the next generation of wireless communication. This article evaluates the performance of the FSO system under inverse Gaussian gamma (IGG) fading. A novel closed‐form equation for the cumulative distribution function (CDF) of the received signal‐to‐noise ratio (SNR) is presented by employing an intensity modulation/direct detection (IM/DD) scheme. The analytical expressions for various performance metrics such as outage probability (OP), amount of fading (AOF), and average bit error probability (ABEP) are derived for various digital modulation schemes based on the system's probability density function (PDF) and CDF. Additionally, this article presents an upper bound on OP and asymptotic analysis for the performance metrics to gain deeper insights. It is revealed that the small‐scale eddy turbulence parameter can affect the diversity order by a factor of β/2. The results demonstrate that atmospheric turbulence considerably reduces the system's performance. Finally, Monte‐Carlo simulation is performed to ascertain the correctness of the derived mathematical expressions.

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A comprehensive toolbox for the gamma distribution: The gammadist package

Cited by 9 publications

References 35 publications

Testing multiple dispersion effects from unreplicated order‐of‐addition experiments

Testing multiple dispersion effects from unreplicated order‐of‐addition experiments

Symmetry of gamma distribution data about the mean after processing with EWMA function

Performance Analysis of Free Space Optical System Over Inverse Gaussian Gamma Turbulence Channel

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