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<p>Skewed data often appear in actuarial, biological, medical studies, clinical trials, industrial and engineering fields. To model such skewed data, a lot of skew distributions including skew normal/<i>t</i>/logistic have been proposed to investigate the relationship between the response variable and a set of explanatory variables. However, to our best knowledge, there exists few mean regression model based on skew distributions. This paper applies the <i>Type I generalized logistic</i> (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="362_2025_1737_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {GL}^{\text{(I)}}\)</EquationSource> </InlineEquation>) distribution to construct a mean regression model for fitting skewed data. First, we reparameterize the shape, location and scale parameters to ensure the existence of <i>maximum likelihood estimators</i> (MLEs) of parameters even for the embedded model problem. Next, we develop a new <i>quadratic lower bound</i> (QLB) algorithm with monotone convergence to calculate MLEs of parameters, which has been proved to be computationally efficient even for the high-dimensional vector of covariates with correlated components in simulations. A real data set is analyzed to illustrate the proposed methods.</p>

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Mean regression model for Type I generalized logistic distribution with a QLB algorithm

  • 期刊论文

  • 发表日期：

    2025年8月6日

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  • Xun-Jian Li,
  • Jiajuan Liang,
  • Guo-Liang Tian,
  • Man-Lai Tang,
  • Jianhua Shi

摘要

Skewed data often appear in actuarial, biological, medical studies, clinical trials, industrial and engineering fields. To model such skewed data, a lot of skew distributions including skew normal/t/logistic have been proposed to investigate the relationship between the response variable and a set of explanatory variables. However, to our best knowledge, there exists few mean regression model based on skew distributions. This paper applies the Type I generalized logistic ( \(\text {GL}^{\text{(I)}}\) ) distribution to construct a mean regression model for fitting skewed data. First, we reparameterize the shape, location and scale parameters to ensure the existence of maximum likelihood estimators (MLEs) of parameters even for the embedded model problem. Next, we develop a new quadratic lower bound (QLB) algorithm with monotone convergence to calculate MLEs of parameters, which has been proved to be computationally efficient even for the high-dimensional vector of covariates with correlated components in simulations. A real data set is analyzed to illustrate the proposed methods.