Gaussian integrals and Rice series in crossing distributions : to compute the distribution of maxima and other features of Gaussian processes
(2019) In Statistical Science 34(1). p.100128 Abstract (Swedish)
 We describe and compare how methods based on the classical
Rice’s formula for the expected number, and higher moments, of level crossings
by a Gaussian process stand up to contemporary numerical methods to
accurately deal with crossing related characteristics of the sample paths.
We illustrate the relative merits in accuracy and computing time of the Rice
moment methods and the exact numerical method, developed since the late
1990s, on three groups of distribution problems, the maximum over a finite
interval and the waiting time to first crossing, the length of excursions over a
level, and the joint period/amplitude of oscillations.
We also treat the notoriously difficult problem of dependence... (More)  We describe and compare how methods based on the classical
Rice’s formula for the expected number, and higher moments, of level crossings
by a Gaussian process stand up to contemporary numerical methods to
accurately deal with crossing related characteristics of the sample paths.
We illustrate the relative merits in accuracy and computing time of the Rice
moment methods and the exact numerical method, developed since the late
1990s, on three groups of distribution problems, the maximum over a finite
interval and the waiting time to first crossing, the length of excursions over a
level, and the joint period/amplitude of oscillations.
We also treat the notoriously difficult problem of dependence between successive
zero crossing distances. The exact solution has been known since at
least 2000, but it has remained largely unnoticed outside the ocean science
community.
Extensive simulation studies illustrate the accuracy of the numerical methods.
As a historical introduction an attempt is made to illustrate the relation
between Rice’s original formulation and arguments and the exact numerical
methods. (Less)  Abstract
 We describe and compare how methods based on the classical Rice’s formula for the expected number, and higher moments, of level crossings by a Gaussian process stand up to contemporary numerical methods to accurately deal with crossing related characteristics of the sample paths.
We illustrate the relative merits in accuracy and computing time of the Rice moment methods and the exact numerical method, developed since the late 1990s, on three groups of distribution problems, the maximum over a finite interval and the waiting time to first crossing, the length of excursions over a level, and the joint period/amplitude of oscillations.
We also treat the notoriously difficult problem of dependence between successive zero... (More)  We describe and compare how methods based on the classical Rice’s formula for the expected number, and higher moments, of level crossings by a Gaussian process stand up to contemporary numerical methods to accurately deal with crossing related characteristics of the sample paths.
We illustrate the relative merits in accuracy and computing time of the Rice moment methods and the exact numerical method, developed since the late 1990s, on three groups of distribution problems, the maximum over a finite interval and the waiting time to first crossing, the length of excursions over a level, and the joint period/amplitude of oscillations.
We also treat the notoriously difficult problem of dependence between successive zero crossing distances. The exact solution has been known since at least 2000, but it has remained largely unnoticed outside the ocean science community.
Extensive simulation studies illustrate the accuracy of the numerical methods. As a historical introduction an attempt is made to illustrate the relation between Rice’s original formulation and arguments and the exact numerical methods.
(Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/e4f7936e1f0f4223a59e17af53ca3b73
 author
 Lindgren, Georg ^{LU}
 organization
 publishing date
 2019
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 computational statistics, distribution of maximum, Durbin’s formula, excursion length distribution, first passage, independent interval assumption, level crossings, multivariate normal probabilities, pe riod/amplitude distribution, Rice’s formula, RIND program, statistical computation, stochastic process, successive crossing distance distribution, truncated normal moments, Wafo toolbox
 in
 Statistical Science
 volume
 34
 issue
 1
 pages
 100  128
 publisher
 IMS
 external identifiers

 scopus:85065490257
 ISSN
 08834237
 DOI
 10.1214/18STS662
 language
 English
 LU publication?
 yes
 id
 e4f7936e1f0f4223a59e17af53ca3b73
 date added to LUP
 20181213 12:33:30
 date last changed
 20191113 05:22:43
@article{e4f7936e1f0f4223a59e17af53ca3b73, abstract = {We describe and compare how methods based on the classical Rice’s formula for the expected number, and higher moments, of level crossings by a Gaussian process stand up to contemporary numerical methods to accurately deal with crossing related characteristics of the sample paths.<br/><br/>We illustrate the relative merits in accuracy and computing time of the Rice moment methods and the exact numerical method, developed since the late 1990s, on three groups of distribution problems, the maximum over a finite interval and the waiting time to first crossing, the length of excursions over a level, and the joint period/amplitude of oscillations.<br/><br/>We also treat the notoriously difficult problem of dependence between successive zero crossing distances. The exact solution has been known since at least 2000, but it has remained largely unnoticed outside the ocean science community.<br/><br/>Extensive simulation studies illustrate the accuracy of the numerical methods. As a historical introduction an attempt is made to illustrate the relation between Rice’s original formulation and arguments and the exact numerical methods.<br/>}, author = {Lindgren, Georg}, issn = {08834237}, keyword = {computational statistics,distribution of maximum,Durbin’s formula,excursion length distribution,first passage,independent interval assumption,level crossings,multivariate normal probabilities,pe riod/amplitude distribution,Rice’s formula,RIND program,statistical computation,stochastic process,successive crossing distance distribution,truncated normal moments,Wafo toolbox}, language = {eng}, number = {1}, pages = {100128}, publisher = {IMS}, series = {Statistical Science}, title = {Gaussian integrals and Rice series in crossing distributions : to compute the distribution of maxima and other features of Gaussian processes}, url = {http://dx.doi.org/10.1214/18STS662}, volume = {34}, year = {2019}, }