The unit log–log distribution: a new unit distribution with alternative quantile regression modeling and educational measurements applications

Korkmaz, Mustafa Ç.; Korkmaz, Zehra Sedef

doi:10.1080/02664763.2021.2001442

Cited by 43 publications

(39 citation statements)

References 52 publications

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“…There are numerous works based on (unit) distributions, extending a model and applying it to several areas (Korkmaz & Korkmaz 2021. In this work, we introduced and showed the competitiveness of the AU distribution, especially for data with a range greater than 0.4, or which present high asymmetry and low decay.…”

Section: Discussionmentioning

confidence: 99%

“…In the case of rates and proportions processes, as well as other processes whose variable of interest 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 double-bounded data. Among the existing unit distributions, we can cite the power distribution, beta distribution (Ferrari & Cribari-Neto 2004), Kumaraswamy distribution (Kumaraswamy 1980), unit-logistic distribution (Tadikamalla & Johnson 1982), simplex distribution (Barndorff-Nielsen & Jørgensen 1991), unit-Weibull distribution (Mazucheli et al 2018, Mazucheli et al 2020, unit-Lindley distribution (Mazucheli et al 2019), unit-half normal distribution (Bakouch et al 2021), unit log-log distribution (Korkmaz & Korkmaz 2021), modified Kumaraswamy and reflected modified Kumaraswamy distributions (Sagrillo et al 2021), unit-Teissier distribution (Krishna et al 2022), unit extended Weibull families of distributions (Guerra et al 2021), unit folded normal distribution , unit-Chen distribution (Korkmaz, Altun, Chesneau & Yousof 2022), and Marshall-Olkin reduced Kies distribution (Afify et al 2022). Despite the applicability of the unit distributions in double-bounded variables, another important fact is that the interval estimation for the parameter may also be limited in a domain (like positive real number).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extending normality: A case of unit distribution generated from the moments of the standard normal distribution

Concha-Aracena¹,

Barrios-Blanco²,

Elal-Olivero³

et al. 2022

Preprint

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This article presents an important theorem, which shows that from the moments of the standard normal distribution one can generate density functions originating a family of models. Additionally, we discussed that different random variable domains are achieved with transformations. For instance, we adopted the moment of order two, from the proposed theorem, and transformed it, which allowed us to exemplify this class as unit distribution. We named it as Alpha-Unit (AU) distribution, which contains a single positive parameter α (AU(α) ∈ [0, 1]). We presented its properties and showed two estimation methods for the α parameter, the maximum likelihood estimator (MLE) and uniformly minimum-variance unbiased estimator (UMVUE) methods. In order to analyze the statistical consistency of the estimators, a Monte Carlo simulation study was carried out, where the robustness was demonstrated. As real-world application, we adopted two sets of unit data, the first regarding the dynamics of Chilean inflation in the post-military period, and the other regarding the daily maximum relative humidity of the air in the Atacama Desert. In both cases shown, the AU model is competitive, whenever the data present a range greater than 0.4 and extremely heavy asymmetric tail. We compared our model against other commonly used unit models, such as the beta, Kumaraswamy, logit-normal, simplex, unit-half-normal, and unit-Lindley distributions.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extending normality: A case of unit distribution generated from the moments of the standard normal distribution

Concha-Aracena¹,

Barrios-Blanco²,

Elal-Olivero³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“… 2021d ), unit-folded normal (Korkmaz et al. 2022b ), unit-log-log (Korkmaz and Korkmaz 2022 ), unit arcsecant hyperbolic Weibull (Korkmaz et al. 2022a ) and Vasicek (Mazucheli et al.…”

Section: Introductionmentioning

confidence: 99%

The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications

et al. 2022

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In this paper, we propose and derive a new regression model for response variables defined on the open unit interval. By reparameterizing the unit generalized half-normal distribution, we get the interpretation of its location parameter as being a quantile of the distribution. In addition, we can evaluate effects of the explanatory variables in the conditional quantiles of the response variable as an alternative to the Kumaraswamy quantile regression model. The suitability of our proposal is demonstrated with two simulated examples and two real applications. For such data sets, the obtained fits of the proposed regression model are compared with that provided by a Kumaraswamy regression model.

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“…are united. Some unit distributions studied in recent years can be given as follows [5][6][7][8][9][10]. In this study, the Burr-Hatke distribution is united.…”

Section: Introductionmentioning

confidence: 99%

“…As an alternative to beta regression, new quantile-based regression models are constructed. Some of these regression models can be reported as [8,9,[15][16][17]. In this paper, a new quantile regression model is introduced based on the new model.…”

Section: Introductionmentioning

confidence: 99%

Unit Burr-Hatke Distribution With a New Quantile Regression Model

SAĞLAM

Karakaya

2022

J. Sci. Arts

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In this study, a new distribution is introduced. The Burr-Hatke distribution is considered the baseline distribution. Since the baseline distribution has one parameter, the new unit distribution also has one parameter. Some distributional properties such as moments, coefficients of skewness and kurtosis, stochastic ordering, etc. of the new distribution are studied. Five estimators such as maximum likelihood, least squares, weighted least squares, Anderson-Darling, and Cramer-von Mises are examined to estimate the unknown parameter of the new model. The performances of the estimators are analyzed according to the bias and mean square error criteria calculated by Monte Carlo simulation. Two numerical data analyses are performed. A new quantile regression model is also introduced based on the new distribution as an alternative to beta and Kumaraswamy regression. A Monte Carlo simulation is also conducted for the new regression model.

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The unit log–log distribution: a new unit distribution with alternative quantile regression modeling and educational measurements applications

Abstract: This Section gives some distributional properties of the ULL distribution to know its properties in a better way.

Cited by 43 publications

References 52 publications

Extending normality: A case of unit distribution generated from the moments of the standard normal distribution

Extending normality: A case of unit distribution generated from the moments of the standard normal distribution

The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications

Unit Burr-Hatke Distribution With a New Quantile Regression Model

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