GS-distributions: A new family of distributions for continuous unimodal variables

Muiño, José M.; Voit, Eberhard O.; Sorribas, Albert

doi:10.1016/j.csda.2005.04.016

Cited by 10 publications

(6 citation statements)

References 24 publications

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“…Muiño et al45 pointed out several limitations of the S ‐distributions, such as the family only includes one symmetric distribution, namely logistic with g = 1 and k = 1, neither does the family properly accommodate distributions with heavy tails, nor finite right tails. An extension45 of the S ‐distribution, GS ‐distribution, was given as The GS ‐distribution has five parameters. Parameter α is a scale parameter playing the same role as in S ‐distribution, parameters g , k , and γ are shape parameters, and the initial value x 0 for a given F 0 is a position parameter.…”

Section: Some Methods Prior To 1980mentioning

confidence: 99%

“…Parameter α is a scale parameter playing the same role as in S ‐distribution, parameters g , k , and γ are shape parameters, and the initial value x 0 for a given F 0 is a position parameter. Further details45 on using the GS ‐distributions to approximate commonly used distributions such as Weibull, lognormal, and others were discussed.…”

Section: Some Methods Prior To 1980mentioning

confidence: 99%

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Methods for generating families of univariate continuous distributions in the recent decades

Lee

Famoye

Alzaatreh

2013

WIREs Computational Stats

150

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There has been a renewed interest in developing more flexible statistical distributions in recent decades. A major milestone in the methods for generating statistical distributions is undoubtedly the system of differential equation approach. There is a recent renewed interest in generating skewed distributions. Generally speaking, the methods developed prior to 1980s may be summarized into three categories: (1) method of differential equation, (2) method of transformation, and (3) quantile method. Techniques developed since 1980s may be categorized as ‘methods of combination’ for the reason that these methods attempt to combine existing distributions into new distributions or adding new parameters to an existing distribution. This article discusses five general methods of combination and their variations. These five are (1) method of generating skew distributions, (2) method of adding parameters (e.g., exponentiation), (3) beta generated method, (4) transformed‐transformer method, and (5) composite method. WIREs Comput Stat 2013, 5:219–238. doi: 10.1002/wics.1255 This article is categorized under: Algorithms and Computational Methods > Random Number Generation Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

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Section: Some Methods Prior To 1980mentioning

confidence: 99%

Section: Some Methods Prior To 1980mentioning

confidence: 99%

Methods for generating families of univariate continuous distributions in the recent decades

Lee

Famoye

Alzaatreh

2013

WIREs Computational Stats

150

View full text Add to dashboard Cite

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“…We subsequently discuss how the coverage factors k p and k p of the expanded uncertainty of the measurand Y can be determined from the fitted distribution. The distributions considered are (i) the Pearson family of distributions [5,6] that satisfies a given differential equation; (ii) the Tukey's lambda-distribution [7] that is generated from a uniform random variable; (iii) the Tukey's gh-distribution [8] that is generated based on transformation of a standard normal random variable and (iv) the GS-distribution [9] in which its PDF is approximated as a function of its cumulation distribution function.…”

Section: Y Ymentioning

confidence: 99%

Evaluating expanded uncertainty in measurement with a fitted distribution

Sim¹,

Lim²

2008

Metrologia

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It is recommended in the internationally adopted standard GUM that the measurement result of a measurand Y , determined from input quantities through a known functional relationship, should be reported as an uncertainty interval with a specific level of confidence. The uncertainty intervals discussed in GUM are evaluated by assuming that the measurements of Y follow a normal or t distribution. However, in practice, the resulting measurements of Y tend to follow an asymmetric distribution. This communication reviews some generalized univariate distributions that can be fitted to the measurements of Y based on its shape in terms of its coefficients of skewness and kurtosis. The uncertainty interval of the measurand is then evaluated from the fitted distribution. Examples are given to illustrate the use of these distributions in evaluating the expanded uncertainty in measurement.

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“…Examples are derivations of the Pearson family of distributions, which have been shown to satisfy differential equations—the normal, beta, gamma, and Student's t ‐distribution being specific cases (Pearson, 1895). A more recent contribution of this type is provided by Voit (1992) who introduced S‐distributions, which include exponential, logistic, and uniform distributions as special cases; see also Savageau (1982), Rust and Voit (1990), Yu and Voit (2006), Muino, Voit, and Sorribas (2006), and the references therein. Further, it turns out that there is a linear differential operator corresponding to most of the densities one sees in classical textbooks.…”

Section: Introductionmentioning

confidence: 99%

Differential equations in data analysis

Dattner

2020

WIREs Computational Stats

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Differential equations have proven to be a powerful mathematical tool in science and engineering, leading to better understanding, prediction, and control of dynamic processes. In this paper, we review the role played by differential equations in data analysis. More specifically, we consider the intersection between differential equations and data analysis in the light of modern statistical learning methodologies. This article is categorized under: Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical Models > Nonlinear Models

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GS-distributions: A new family of distributions for continuous unimodal variables

Cited by 10 publications

References 24 publications

Methods for generating families of univariate continuous distributions in the recent decades

Methods for generating families of univariate continuous distributions in the recent decades

Evaluating expanded uncertainty in measurement with a fitted distribution

Differential equations in data analysis

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