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

Korkmaz, Mustafa Ç.; Altun, Emrah; Alizadeh, Morad; El-Morshedy, Mahmoud

doi:10.3390/math9212634

Cited by 13 publications

(8 citation statements)

References 28 publications

(36 reference statements)

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“…. ., y n ) > the vector of n observations of a response variable and X the covariates matrix like in (10). In statistical learning methods, a training data set is the observations set in which a model is initially adjusted.…”

Section: Plos Onementioning

confidence: 99%

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Another unit Burr XII quantile regression model based on the different reparameterization applied to dropout in Brazilian undergraduate courses

et al. 2022

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In many practical situations, there is an interest in modeling bounded random variables in the interval (0, 1), such as rates, proportions, and indexes. It is important to provide new continuous models to deal with the uncertainty involved by variables of this type. This paper proposes a new quantile regression model based on an alternative parameterization of the unit Burr XII (UBXII) distribution. For the UBXII distribution and its associated regression, we obtain score functions and observed information matrices. We use the maximum likelihood method to estimate the parameters of the regression model, and conduct a Monte Carlo study to evaluate the performance of its estimates in samples of finite size. Furthermore, we present general diagnostic analysis and model selection techniques for the regression model. We empirically show its importance and flexibility through an application to an actual data set, in which the dropout proportion of Brazilian undergraduate animal sciences courses is analyzed. We use a statistical learning method for comparing the proposed model with the beta, Kumaraswamy, and unit-Weibull regressions. The results show that the UBXII regression provides the best fit and the most accurate predictions. Therefore, it is a valuable alternative and competitive to the well-known regressions for modeling double-bounded variables in the unit interval.

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Section: Plos Onementioning

confidence: 99%

“…[8,9] proposed the unit Burr XII and reflected unit Burr XII, respectively. Other quantile regressions were introduced by [10,11], and [12]. One may also see [13][14][15][16] for unit regressions applied to educational measurements.…”

Section: Introductionmentioning

confidence: 99%

Another unit Burr XII quantile regression model based on the different reparameterization applied to dropout in Brazilian undergraduate courses

et al. 2022

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“… 2022 ), unit-log exponential power (Korkmaz et al. 2021d ), unit-folded normal (Korkmaz et al. 2022b ), unit-log-log (Korkmaz and Korkmaz 2022 ), unit arcsecant hyperbolic Weibull (Korkmaz 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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“…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 Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model

Cited by 13 publications

References 28 publications

Another unit Burr XII quantile regression model based on the different reparameterization applied to dropout in Brazilian undergraduate courses

Another unit Burr XII quantile regression model based on the different reparameterization applied to dropout in Brazilian undergraduate courses

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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