Parameter Estimation And Application Of The Asymmetric Three Parameters Student-t Distribution And The Alpha Skew Generalized Error Distribution

When fitting the asymmetric and heavy-tailed data in actual operation,we prefer to construct a more complex distribution.function rather than select a continuous and symmetrical distribution.In other words,we use to adding parameters to the distribution such as normal distribution and t distribution and make the new distribution accurately fit complex real-world data.The methods of adding parameters are plentiful and different and they can be roughly divided into "change skewness","change tail",and"change skewness and tail simultaneously".Based on the student-t distribution and the generalized error distribution,this paper constructs two special distribution:The asymmetric three parameters Student-t distributions and The alpha-skew generalized error distributions.In this paper,we deduce their cumulative distribution function,quantile function,origin moment expression,random variable sampling algorithm and other statistical properties.And this paper studies three methods of parameter estimation including the moment estimation,maximum likelihood estimation and Bayesian estimation.Simulation data are generated by sampling algorithm for purpose of verifying and comparing these three parameter estimation methods.Finally,the two distributions are individually used to fit two examples.The results show that these two distributions have better fitting ability in terms of asymmetric and heavy-tailed data than other distributions.