A study of generalized logistic distributions

Nassar, Mohamed A.; Elmasry, A.

doi:10.1016/j.joems.2012.08.011

Cited by 17 publications

(13 citation statements)

References 18 publications

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“…The characteristic function of a given random variable can be obtained by calculating the Fourier transform of its probability density function. The characteristic function of a GLD random variable is widely known in the literature [12]. On the other hand, in order to better understand the scaling process performed to generate the variable Y i = b i X i , the characteristic function of Y i shall be obtained explicitly.…”

Section: The Characteristic Function Ofmentioning

confidence: 99%

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Linear Combination and Reliability of Generalized Logistic Random Variables

Ozelim

Rathie

2019

Eur. J. Pure Appl. Math.

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Experimental random data, in general, present a skewed behaviour. Thus, asymmetrical generalized distributions are of interest. The generalized logistic distributions (GLDs) are good candidates to model skewed data because their probability density functions (p.d.f.) and characteristic functions are mathematically simple. In this paper, exact expressions in terms of the H-function are, for the first time, derived for the p.d.f. and for the cummulative distribution function of the linear combination of GLDs of type IV with different location, scale and shape parameters. Also, exact and approximate expressions are derived for $R=P(X<Y)$. Numerical examples illustrate the correctness of the expressions derived.

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Section: The Characteristic Function Ofmentioning

confidence: 99%

“…Applications of this kind of random variable are easily seen in the literature. A complete study has been recently performed in [12]. For example, regarding applied scientists, [4] employed generalized logistic models to perform flood analysis in partial duration series.…”

Section: Introductionmentioning

confidence: 99%

Linear Combination and Reliability of Generalized Logistic Random Variables

Ozelim

Rathie

2019

Eur. J. Pure Appl. Math.

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“…Choosing between I β and I N One initial complication is that there is no "obvious" way to choose between I N and I β . Figure 1 illustrates the similarity between the densities of the two families, a fact that is discussed in [14]. I N is attractive on the grounds that Gaussians are often easy to work with, but we can also motivate its usage by appealing to the principle of maximum entropy.…”

Section: Likelihoodmentioning

confidence: 99%

Hierarchical Bayesian Bradley–Terry for applications in Major League Baseball

Phelan¹

2018

Math. Appl.

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Abstract. A common problem faced in statistical inference is drawing conclusions from paired comparisons, in which two objects compete and one is declared the victor. A probabilistic approach to such a problem is the Bradley-Terry model [5,20], first studied by Zermelo in 1929 and rediscovered by Bradley and Terry in 1952. One obvious area of application for such a model is sporting events, and in particular Major League Baseball. With this in mind, we describe a hierarchical Bayesian version of Bradley-Terry suitable for use in ranking and prediction problems, and compare results from these application domains to standard maximum likelihood approaches. Our Bayesian methods outperform the MLE-based analogues, while being simple to construct, implement, and interpret.

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“…In fact, the literature on both the theory and applications based on the logistic distribution is so vast it would be unthinkable to reference even a fraction of it. Some recent authors like [14], [11], [9], [8] and [10] provide extensive studies on the characteristics of generalized logistic distributions, somehow answering the ever increasing interest in the logistic family of distributions. Indeed, applications abound that make use of both the standard logistic regression model and the so-called generalized logistic regression model, as can be seen in [13] and [12].…”

Section: Necla Gündüz and Ernest Fokouémentioning

confidence: 99%

On the predictive properties of binary link functions

FOKOUÉ

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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ON THE PREDICTIVE PROPERTIES OF BINARY LINK FUNCTIONS NECLA GÜNDÜZ AND ERNEST FOKOUÉAbstract. This paper provides a theoretical and computational justi…cation of the long held claim of the similarity of the probit and logit link functions often used in binary classi…cation. Despite this widespread recognition of the strong similarities between these two link functions, very few (if any) researchers have dedicated time to carry out a formal study aimed at establishing and characterizing …rmly all the aspects of the similarities and di¤erences. This paper proposes a de…nition of both structural and predictive equivalence of link functions-based binary regression models, and explores the various ways in which they are either similar or dissimilar. From a predictive analytics perspective, it turns out that not only are probit and logit perfectly predictively concordant, but the other link functions like cauchit and complementary log log enjoy very high percentage of predictive equivalence. Throughout this paper, simulated and real life examples demonstrate all the equivalence results that we prove theoretically.

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A study of generalized logistic distributions

Cited by 17 publications

References 18 publications

Linear Combination and Reliability of Generalized Logistic Random Variables

Linear Combination and Reliability of Generalized Logistic Random Variables

Hierarchical Bayesian Bradley–Terry for applications in Major League Baseball

On the predictive properties of binary link functions

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