Parameter estimation for univariate Skew-Normal distribution based on the modified empirical characteristic function

Abstract

Parameter estimation for the skew-normal distribution is challenging, since the profile likelihood function of shape parameter has a stationary point at zero, which hampers the use of traditional methods, such as maximum likelihood method. We present a modified empirical characteristic function method to perform parameter estimation for the skew-normal distribution. The proposed approach is flexible and easy to implement. We show that the estimators converge to the true values in probability. The simulation study and data analysis suggest that the proposed method performs well, even for the case of small sample size.

Keywords:

• Skew-normal distribution
• empirical characteristic function
• M-estimator
• bootstrap

Additional information

Funding

The research is supported by National Natural Science Foundation of China (11671303) and Foundation of Zhejiang Province(LY19A010014).