Estimation and Simulation for the M-Wright Function

Abstract

In this article, a structural form of an M-Wright distributed random variable is derived. The mixture representation then led to a random number generation algorithm. A formal parameter estimation procedure is also proposed. This procedure is needed to make the M-Wright function usable in practice. The asymptotic normality of the estimator is established as well. The estimator and the random number generation algorithm are then tested using synthetic data.

Keywords:

• Bootstrap
• Estimation
• Method-of-moments
• M-Wright function
• Stable distribution
• Wright function

2000 Mathematics Subject Classification:

• Primary 62E15
• Secondary 97K80, 97K60, 60G22, 62E15, 62E20, 62G05

Acknowledgment

The author is highly grateful to the Editor and the three reviewers for their insightful comments and valuable suggestions that significantly improved the article.