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Optimal Multistage Sampling in a Boundary-Crossing Problem
Asymptotic Brownian motion Group sequential Multistage Optimality
2011/6/17
Brownian motion with known positive drift is sampled in stages until
it crosses a positive boundary a. A family of multistage samplers that con-
trol the expected overshoot over the boundary by vary...
Level crossing and local time for regularized Gaussian processes
Level crossing local time regularized Gaussian processes
2009/9/22
Let (X,,t~ [0, 11) be a oentred stationary Gaussian
process defined on (D,A , P) with covariance function satisfying
Define the regularized process
X' = cp, * X and YE = Xc/oe, where CT~ = var Xf ,...
This paper proposes a method to address the longstanding problem of lack of
monotonicity in estimation of conditional and structural quantile functions, also known as
the quantile crossing problem. ...
Kendall's identity for the first crossing time revisited
skip-free Levy process first crossing time change of measure
2009/5/4
We give a new relatively compact proof of the famous identity for the distribution of the first hitting time of a linear boundary by a skip-free process with stationary independent increments. The pro...
Analytic crossing probabilities for certain barriers by Brownian motion
Brownian motion boundary-crossing probability moving barrier first hitting time density last exit time density Schwartz distribution
2010/4/28
We calculate crossing probabilities and one-sided last exit time
densities for a class of moving barriers on an interval [0,T] via Schwartz
distributions. We derive crossing probabilities and first ...