A flexible probability model for proportion data: Unit-half-normal distribution

Bakouch, Hassan S.; Nik, Ali Saadati; Asgharzadeh, A.; Salinas, Hugo S.

doi:10.1080/23737484.2021.1882355

Cited by 22 publications

(15 citation statements)

References 21 publications

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“…Thus, this article will propose an interesting and useful alternative to the previously mentioned control charts for monitoring processes with continuous data in the unit interval (e.g., rates, proportions or indices), the so-called unit-Lindley chart. Other works, such as [12][13][14][15], explored the unit transformation and showed the importance of the unit distributions class. Moreover, stochastic phenomena can be approximated, with a clear advantage and simplicity grounds, by summarizing a large quantity of data by a few numerical values, in the form of parametric models, enabling the modeller to learn about observable phenomena [16].…”

Section: Introductionmentioning

confidence: 99%

Water Particles Monitoring in the Atacama Desert: SPC Approach Based on Proportional Data

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Ferreira

Nascimento

et al. 2021

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Statistical monitoring tools are well established in the literature, creating organizational cultures such as Six Sigma or Total Quality Management. Nevertheless, most of this literature is based on the normality assumption, e.g., based on the law of large numbers, and brings limitations towards truncated processes as open questions in this field. This work was motivated by the register of elements related to the water particles monitoring (relative humidity), an important source of moisture for the Copiapó watershed, and the Atacama region of Chile (the Atacama Desert), and presenting high asymmetry for rates and proportions data. This paper proposes a new control chart for interval data about rates and proportions (symbolic interval data) when they are not results of a Bernoulli process. The unit-Lindley distribution has many interesting properties, such as having only one parameter, from which we develop the unit-Lindley chart for both classical and symbolic data. The performance of the proposed control chart is analyzed using the average run length (ARL), median run length (MRL), and standard deviation of the run length (SDRL) metrics calculated through an extensive Monte Carlo simulation study. Results from the real data applications reveal the tool’s potential to be adopted to estimate the control limits in a Statistical Process Control (SPC) framework.

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Section: Introductionmentioning

confidence: 99%

Water Particles Monitoring in the Atacama Desert: SPC Approach Based on Proportional Data

Fonseca

Ferreira

Nascimento

et al. 2021

Axioms

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“…In the case of rates and proportions processes, whereas the observed variable assumes values in the range (0, 1), there is a well-represented class of models, the unit distributions family, which deals with this type of sensor data, but are often univariate and not extended, in their inference, to some regression structures (see, e.g., [2][3][4][5]). Regression structures, in probabilistic modeling, can provide a flexible set of tools for examining such associations, while enabling, either, potentially confounding effects of other factors, or interaction effects for Statistical Process Control (SPC) tools [6].…”

Section: Introductionmentioning

confidence: 99%

Unraveling water monitoring association towards weather attributes for response proportions data: A unit-Lindley learning

et al. 2022

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Learning techniques involve unraveling regression structures, which aim to analyze in a probabilistic frame the associations across variables of interest. Thus, analyzing fraction and/or proportion data may not be adequate with standard regression procedures, since the linear regression models generally assume that the dependent (outcome) variable is normally distributed. In this manner, we propose a statistical model called unit-Lindley regression model, for the purpose of Statistical Process Control (SPC). As a result, a new control chart tool was proposed, which targets the water monitoring dynamic, as well as the monitoring of relative humidity, per minute, of Copiapó city, located in Atacama Desert (one of the driest non-polar places on Earth), north of Chile. Our results show that variables such as wind speed, 24-hour temperature variation, and solar radiation are useful to describe the amount of relative humidity in the air. Additionally, Information Visualization (InfoVis) tools help to understand the time seasonality of the water particle phenomenon of the region in near real-time analysis. The developed methodology also helps to label unusual events, such as Camanchaca, and other water monitoring-related events.

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“…Similarly, [8] used X = T/(T + 1) transformation on the improved second-degree Lindley (ISDL) distribution and resulting distribution was called as unit-ISDL distribution. These approaches have been used many authors such as [9][10][11][12][13][14][15][16][17][18][19] and so on.…”

Section: Introductionmentioning

confidence: 99%

“…The profile log-likelihood (PLL) functions are plotted in Figure 18 for the parameters of the QLEP distribution. According to Figure 18, the estimated parameters are maximizers of the function in (13).…”

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confidence: 99%

The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model

et al. 2021

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Recently, bounded distributions have attracted attention. These distributions are frequently used in modeling rate and proportion data sets. In this study, a new alternative model is proposed for modeling bounded data sets. Parameter estimations of the proposed distribution are obtained via maximum likelihood method. In addition, a new regression model is defined under the proposed distribution and its residual analysis is examined. As a result of the empirical studies on real data sets, it is observed that the proposed regression model gives better results than the unit-Weibull and Kumaraswamy regression models.

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A flexible probability model for proportion data: Unit-half-normal distribution

Cited by 22 publications

References 21 publications

Water Particles Monitoring in the Atacama Desert: SPC Approach Based on Proportional Data

Water Particles Monitoring in the Atacama Desert: SPC Approach Based on Proportional Data

Unraveling water monitoring association towards weather attributes for response proportions data: A unit-Lindley learning

The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model

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