A Double Recursion for Calculating Moments of the Truncated Normal Distribution and its Connection to Change Detection

Moshe Pollak () and Michal Shauly-Aharonov ()
Additional contact information
Moshe Pollak: The Hebrew University of Jerusalem
Michal Shauly-Aharonov: The Hebrew University of Jerusalem

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 3, 889-906

Abstract: Abstract The integral ∫ 0 ∞ x m e − 1 2 ( x − a ) 2 dx ${\int }_{0}^{\infty }x^{m} e^{-\frac {1}{2}(x-a)^{2}}dx$ appears in likelihood ratios used to detect a change in the parameters of a normal distribution. As part of the mth moment of a truncated normal distribution, this integral is known to satisfy a recursion relation, which has been used to calculate the first four moments of a truncated normal. Use of higher order moments was rare. In more recent times, this integral has found important applications in methods of changepoint detection, with m going up to the thousands. The standard recursion formula entails numbers whose values grow quickly with m, rendering a low cap on computational feasibility. We present various aspects of dealing with the computational issues: asymptotics, recursion and approximation. We provide an example in a changepoint detection setting.

Keywords: Changepoint; On-line; Shiryaev–Roberts; Surveillance; 62L10; 62E15; 60E05 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-018-9622-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:21:y:2019:i:3:d:10.1007_s11009-018-9622-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-018-9622-7

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().