Mean regression model for Type I generalized logistic distribution with a QLB algorithm
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 (GLI) 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 computational efficient even for the high dimensional cases with dependent variables. Simulation studies are conducted and a real dataset is analyzed to illustrate the proposed methods.