Sequential probability ratio test for the mode of M-Gaussian distribution

ABSTRACT

Scientific data, as a sequential or a simple random sample, often indicate a unimodal, right-skewed population. For such data, the ubiquitous symmetry assumption and the Gaussian model are inappropriate and in case of high skewness, even corrections using devices such as Box-Cox transformation are inadequate. In such cases, the recently introduced M-Gaussian distribution, which may be described as an R-symmetric Gaussian twin, with its mode as the centrality parameter, can be an appropriate model. In this article, the concept of R-symmetry, the basic properties of the M-Gaussian distribution and some analogies between Gaussian and M-Gaussian distributions are reviewed. Then the sequential probability ratio test (SPRT) for simple a hypothesis about the mode of an M-Gaussian population assuming the dispersion parameter to be known is derived. The average sample number (ASN) and operating characteristic (OC) function are obtained and the robustness properties of the test with respect to the harmonic variance assumption are studied. The results are compared with the existing parallel studies for the mean of the inverse Gaussian (IG) distribution.

KEYWORDS:

• Control chart
• inverse Gaussian distribution
• M-Gaussian distribution
• mode
• R-symmetry
• sequential sampling plan
• SPRT

MATHEMATICS SUBJECT CLASSIFICATION:

• 62L10

Acknowledgments

We express our sincere appreciation to Professor Nitis Mukhopadhyay and the referee for comments that greatly improved the article.