Rice probability functions for level-crossing intervals of speckle intensity fields

Youssef, Néji; Munakata, T.; Takeda, Mitsuo

doi:10.1016/0030-4018(95)00592-7

Cited by 3 publications

(1 citation statement)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Even today, Rice's approximations based on crossing moments continue to nd new applications, i.a. in material science, (Estrade et al, 2012), laser physics and optics, (Youssef et al, 1996), to mention a few. A survey of solved and unsolved crossing problems from science and technology was presented by Munakata (1998).…”

Section: Crossing Distributions Why and Howmentioning

confidence: 99%

Gaussian Integrals and Rice Series in Crossing Distributions—to Compute the Distribution of Maxima and Other Features of Gaussian Processes

Lindgren¹

2019

Statist. Sci.

View full text Add to dashboard Cite

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 compute the statistical distribution of the maximum over a xed interval, the length of excursions above a level, and the geometry of oscillations, and other 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 nite interval and the waiting time to rst crossing, the length of excursions over a level, and the joint period/amplitude of oscillations.We also treat the notoriously dicult 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.MSC 2010 subject classications: Primary 60G17; secondary 60-08, 60G10, 60G70, 65C50.

show abstract

Section: Crossing Distributions Why and Howmentioning

confidence: 99%