Abstract
Examination of skewness makes academics more aware of the importance of accurate statistical analysis. Undoubtedly, most phenomena contain a certain percentage of skewness which resulted to the appearance of what is -called "asymmetry" and, consequently, the importance of the skew normal family . The epsilon skew normal distribution ESN (μ, σ, ε) is one of the probability distributions which provide a more flexible model because the skewness parameter provides the possibility to fluctuate from normal to skewed distribution. Theoretically, the estimation of linear regression model parameters, with an average error value that is not zero, is considered a major challenge due to having difficulties, as no explicit formula to calculate these estimates can be obtained. Practically, values for these estimates can be obtained only by referring to numerical methods. This research paper is dedicated to estimate parameters of the Epsilon Skew Normal General Linear Model (ESNGLM) using an adaptive least squares method, as along with the employment of the ordinary least squares method for estimating parameters of the General Linear Model (GLM). In addition, the coefficient of determination was used as a criterion to compare the models’ preference. These methods were applied to real data represented by dollar exchange rates. The Matlab software was applied in this work and the results showed that the ESNGLM represents a satisfactory model.
Highlights
The families of Location and Scale play a vital role in modeling and statistical analysis
Estimation Results of Epsilon Skew Normal General Linear Model This section calculates the estimated values of the Epsilon Skew Normal General Linear Model. It includes the estimation of the General Linear Model parameter using the Ordinary Least Squares (OLS) method to compare the models preference using the R2
After using MATLAB software and applying numerical algorithm Trust-region-dogleg, the estimated values of Epsilon Skew Normal General Linear Model (ESNGLM) and General Linear Model (GLM) along with the value of R2 for each model are shown in Table-1
Summary
The families of Location and Scale play a vital role in modeling and statistical analysis This reflects the importance of skew distributions in this field. Several methods, including the logarithmic data taking method, Box-Cox conversions and others, have been used to address this weakness. These methods are not sufficient in many applications, especially the biological ones [3]. In such a case, the alternative method is to provide distributions that are consistent with the data to gain more flexible models to adapt to each specific skewness percentage [4]
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