Date of Award
8-28-2013
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Applied Science
First Advisor
Hassan Elsalloukh
Abstract
The Gamma distribution is one of the most popular distributions for reliability and lifetime data and can be used effectively in analyzing positive skewed data. In real life applications, analysts might wish to have distributions for analyzing positive and negative skewed data, therefore, in this century, we have seen a good attention for fitting data using skew distributions, because it allows continuous variations from symmetric to non-symmetric. Some empirical data, especially, finance (prices and returns) and environmental data have peak distributions and involve tail behavior which affects the model assumptions. In this dissertation, we extend two of the symmetric distributions, reflected gamma and reflected inverted gamma distributions, to the Epsilon Skew Gamma (ES�,�,) and Epsilon Skew Inverted Gamma (ESI�,�,) distributions, respectively, based on the idea of mixing two half normal distributions and adding the skewness parameter to these two halves. The ES�,�, distribution is useful for modeling asymmetric data and detecting or controlling outliers from both sides of the distribution. The proposed models, ES�,�, and ESI�,�,, have some advantages: good representative for skewed, peakedness, and bimodality data. Also, it is efficient in estimation and fitting certain cases study. In the process, we derive the main properties of both ES�,�, and ESI�,�, distribution families, including the probability density functions and distribution functions, means, variances, and skewness and kurtosis coefficients. We also estimate the maximum likelihood (MLEs) and moments estimators (MMEs) of the parameters. We derive the moment generating (mgf) and characteristic functions for the ES�,�, distribution. We also derive Fisher information matrices for both ES�,�, and ESI�,�, distributions. Moreover, we develop simple and multiple linear regression models when errors are distributed as ES�,�,. Further, Bayesian models for ES�,�, are developed as alternative models and informative and non-informative priors with hyperparameters are chosen. Finally, Bayesian regression analysis is developed when the error terms are distributed as ES�,�,.
Recommended Citation
Abdulah, Ebtisam Karim, "Bayesian and Classical Regression Models Inference When the Errors Follow Skewed Distributions" (2013). Theses and Dissertations. 447.
https://research.ualr.edu/etd/447
