On bounded range distribution of a Wiener process

Abstract

We present an exact distribution for the bounded range of a Wiener process by using the truncation method of the probability distributions. Rather than deriving some statistical properties of this distribution including reliability properties, moments, stress-strength parameter, order statistics, Bonferroni curve, Lorenz curve, and Gini’s index, a dataset is analyzed to clarify the effectiveness of this distribution.

Keywords:

• Order statistics
• statistical properties of the distribution
• truncated distribution
• Wiener process

MATHEMATICS SUBJECT CLASSIFICATION:

• MSC (2010): 60J65; 60K40; 62E10

Acknowledgments

The authors are very grateful to the Editor in Chief, Associate Editor, and the anonymous referees for their careful reading of the paper, and for suggestions which helped the authors to improve it.

Disclosure statement

No potential conflict of interest was reported by the author(s).