Abstarct: In practice, to analyze real data, assuming normality is not valid in many cases, and the models that can consider the possible real structure of the data should be used. For this purpose, we need flexible distributions for the analysis of non-normal data such as a thick tail, semi-heavy tail, and heavy tail skewed and bimodality. To this end, in this thesis, we introduce some probability distributions that are suitable for analyzing data with the mentioned properties. We first propose two approaches to develop symmetric distributions to the Bimodal-Unimodal symmetric and skewed distributions. Then we describe and evaluate their applications in the robust and spatial linear regression models. In the second part of the thesis, we introduce a new location-scale semi-parametric regression model constructed baxsed on a semi-heavy tailed hyperbolic secant distribution. We develop skewed generalizations of the hyperbolic secant distribution and construct a linear regression model baxsed on them. We also calculate and evaluate the asymptotic behavior of ML estimators of the introduced regression model. Finally, we introduce a multivariate version of the hyperbolic secant distribution.