Testing if a mixture is from a given location–scale family

Abstract

Suppose we observe a random sample from . Here, to the best of our knowledge, we provide the first parametric test that F ₀ is any given cumulative distribution function. The test is based on the first four sample moments and is most practicable when F ₀ is symmetric. Simulation studies suggest that the test compares well with non-parametric alternatives and that it is consistent. A real data application is also presented.

Keywords:

• cumulants
• mixture
• sample moments

Acknowledgements

The authors thank the editor, the associate editor, and the two referees for careful reading and for their comments which greatly improved the paper.