TY - JOUR
T1 - A Double Recursion for Calculating Moments of the Truncated Normal Distribution and its Connection to Change Detection
AU - Pollak, Moshe
AU - Shauly-Aharonov, Michal
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/9/15
Y1 - 2019/9/15
N2 - The integral ∫0∞xme−12(x−a)2dx 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.
AB - The integral ∫0∞xme−12(x−a)2dx 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.
KW - Changepoint
KW - On-line
KW - Shiryaev–Roberts
KW - Surveillance
UR - http://www.scopus.com/inward/record.url?scp=85073027822&partnerID=8YFLogxK
U2 - 10.1007/s11009-018-9622-7
DO - 10.1007/s11009-018-9622-7
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AN - SCOPUS:85073027822
SN - 1387-5841
VL - 21
SP - 889
EP - 906
JO - Methodology and Computing in Applied Probability
JF - Methodology and Computing in Applied Probability
IS - 3
ER -