Confidence intervals for means and variances of nonnormal distributions

Abstract

In this article, we propose new confidence intervals for the population mean and variance, the ratio of two populations variance, and the difference in the arithmetic averages of two populations with nonnormal distribution. Theoretical and practical aspects of the suggested techniques are presented, as well as their comparison with existing methods based on the estimated coverage probability. The suggested confidence intervals give consistent and best coverage in comparison with other methods. In addition, application of presented methods to a data set in domain of auditing and accounting is described and analyzed. The empirical results confirm the Monte Carlo simulation studies, highlighting the superiority of the now proposed methods.

Keywords:

• Coverage probability
• geometric Average
• Monte Carlo simulation

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62E20
• 65C05
• 62P25

Acknowledgements

I would like to thank the Editor-in-Chief Narayanaswamy Balakrishnan and the anonymous referee for their suggestions and comments.

Notes

1 This research topic was suggested by one of the referees.

Additional information

Funding

This work was supported by Fundação para a Ciência e a Tecnologia, Grant UIDB/00315/2020.