The Epsilon-Skew Exponentiated Beta Distribution

摘要

In this dissertation, we develop the Epsilon Skew Exponentiated Beta Distribution. This distribution is a bimodal skew distribution with shape, location, and skewness parameters. This distribution is useful in applications with bimodal data, such as in the biological data. The shape properties and the effects of parameters are discussed. Furthermore, we derived the mode and the expected values, mean and variance. In addition, we derive the moment generating function and develop the likelihood function. Parameter estimates are also developed. Then, we develop a simulation to generate the Epsilon Skew Exponentiated Beta random variables and use this new distribution in real life application examples. We evaluate how this new distribution fits the data as well as we compare the results to results already done using different distributions.