Properties and estimation of asymmetric exponential power distribution

Abstract

a b s t r a c tThe new distribution class, Asymmetric Exponential Power Distribution (AEPD), proposed in this paper generalizes the class of Skewed Exponential Power Distributions (SEPD) in a way that in addition to skewness introduces different decay rates of density in the left and right tails. Our parametrization provides an interpretable role for each parameter. We derive moments and moment-based measures: skewness, kurtosis, expected shortfall. It is demonstrated that a maximum entropy property holds for the AEPD distributions. We establish consistency, asymptotic normality and efficiency of the maximum likelihood estimators over a large part of the parameter space by dealing with the problems created by non-smooth likelihood function and derive explicit analytical expressions of the asymptotic covariance matrix; where the results apply to the SEPD class they enlarge on the current literature. Also we give a convenient stochastic representation of the distribution; our Monte Carlo study illustrates the theoretical results. We also provide some empirical evidence for the usefulness of employing AEPD errors in GARCH type models for predicting downside market risk of financial assets.

Visualizing Type II Error in Normality Tests

“…As we want all distributions to have the same values of and , consider ~ (0; 1; ; ). From the expressions obtained by Zhu and Zinde-Walsh (2009) for ( ) and ( ) follows that:…”

“…Zhu and Zinde-Walsh (2009) show (as a particular case of a more general distribution) a version of the Skewed Exponential Power Distribution (SEPD) that can be adapted to our needs:…”

Analysis of US Sector of Services with a New Fama-French 5-Factor Model

“…In 2017, Li et al [13] added non-normal errors of SSAEPD proposed by Zhu and Zinde-Walsh (2009) [14] and the EGARCH-type volatilities suggested in Nelson (1991) [15] to extend the 5 factor model in Fama and French (2015). …”

Analysis of the Sector of Software & Computer Services with a New Carhart 4-Factor Model

“…Our research falls into the 2nd group and tries to extend the 4-factor model in Carhart (1997). But different from previous researches, instead of introducing different factors, we use a non-normal error of SSAEPD proposed by Zhu and Zinde-Walsh (2009) [11], and the EGARCH-type volatility of Nelson (1991) [12]. We denote our new model as C-SSAEPD-EGARCH.…”