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Keywords = unit power-skew-normal distribution

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24 pages, 558 KB  
Article
New Class of Unit-Power-Skew-Normal Distribution and Its Associated Regression Model for Bounded Responses
by Guillermo Martínez-Flórez, Rafael B. Azevedo-Farias and Roger Tovar-Falón
Mathematics 2022, 10(17), 3035; https://doi.org/10.3390/math10173035 - 23 Aug 2022
Cited by 7 | Viewed by 1856
Abstract
Several papers on distributions to model rates and proportions have been recently published; their fitting in numerous instances is better than the alternative beta distribution, which has been the distribution to follow when it is necessary to quantify the average of a response [...] Read more.
Several papers on distributions to model rates and proportions have been recently published; their fitting in numerous instances is better than the alternative beta distribution, which has been the distribution to follow when it is necessary to quantify the average of a response variable based on a set of covariates. Despite the great usefulness of this distribution to fit the responses on the (0,1) unit interval, its relevance loses objectivity when the interest is quantifying the influence of these covariates on the quantiles of the variable response in (0,1); being the most critical situation when the distribution presents high asymmetry and/or kurtosis. The main objective of this work is to introduce a distribution for modeling rates and proportions. The introduced distribution is obtained from the alpha-power extension of the skew–normal distribution, which is known in the literature as the power–skew–normal distribution. Full article
(This article belongs to the Special Issue Current Developments in Theoretical and Applied Statistics)
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20 pages, 425 KB  
Article
Modeling Proportion Data with Inflation by Using a Power-Skew-Normal/Logit Mixture Model
by Guillermo Martínez-Flórez, Hector W. Gomez and Roger Tovar-Falón
Mathematics 2021, 9(16), 1989; https://doi.org/10.3390/math9161989 - 20 Aug 2021
Cited by 2 | Viewed by 2503
Abstract
Rate or proportion data are modeled by using a regression model. The considered regression model can be used for studying phenomena with a response on the (0, 1), [0, 1), (0, 1], or [0, 1] intervals. To connect the response variable with the [...] Read more.
Rate or proportion data are modeled by using a regression model. The considered regression model can be used for studying phenomena with a response on the (0, 1), [0, 1), (0, 1], or [0, 1] intervals. To connect the response variable with the linear predictor in the regression model, we use a logit link function, which guarantees that the obtained prediction ranges between zero and one in the cases inflated at zero or one (or both). The model is complemented with the assumption that the errors follow a power-skew-normal distribution, resulting in a very flexible model, and with a non-singular information matrix, constituting an advantage over other existing models in the literature. To explain the probability of point mass at the values zero and/or one (inflated part), we used a polytomic logistic model with covariates. The results of two illustrations showed that the proposed model is a better alternative compared to widely known models in the literature. Full article
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