 Firsthittingtime model

In statistics, firsthittingtime models are a subclass of survival models. The first hitting time, also called first passage time, of a set A with respect to an instance of a stochastic process is the time until the stochastic process first enters A.
Contents
Examples
A common example of a firsthittingtime model is a ruin problem, such as Gambler's ruin. In this example, an entity (often described as a gambler or an insurance company) has an amount of money which varies randomly with time, possibly with some drift. The model considers the event that the amount of money reaches 0, representing bankruptcy. The model can answer questions such as the probability that this occurs within finite time, or the mean time until which it occurs.
Firsthittingtime models can be applied to expected lifetimes, of patients or mechanical devices. When the process reaches an adverse threshold state for the first time, the patient dies, or the device breaks down.
Latent vs observable
In many real world applications, the process is latent, or unobservable. When first hitting time models are equipped with regression structures, accommodating covariate data, we call such regression structure Threshold regression. The threshold state, parameters of the process, and even time scale may depend on corresponding covariates.
A firsthittingtime (FHT) model has two underlying components: (1) a parent stochastic process , and (2) a threshold. The first hitting time is defined as the time when the stochastic process first reaches the threshold. It is very important to distinguish whether the sample path of the parent process is latent (i.e., unobservable) or observable, and such distinction is a characteristic of the FHT model. By far, latent processes are most common. To give an example, we can use a Wiener process as the parent stochastic process. Such Wiener process can be defined with the mean parameter , the variance parameter , and the initial value .
See also
References
 Whitmore, G. A. (1986). "First passage time models for duration data regression structures and competing risks", The Statistician, 35, 207–219. JSTOR 2987525
 Whitmore, G. A. (1995). "Estimating degradation by a Wiener diffusion process subject to measurement error", Lifetime Data Analysis, 1, 307319.
 Whitmore, G. A., M. J. Crowder and J. F. Lawless (1998). "Failure inference from a marker process based on a bivariate Wiener model", Lifetime Data Analysis, 4, 229251.
 Redner, S (2001). A Guide to FirstPassage Processes, Cambridge University Press. ISBN 0521652480
Categories: Survival analysis
 Regression analysis
 Statistical models
Wikimedia Foundation. 2010.
Look at other dictionaries:
Model aircraft — A die cast Boeing 747 400 model. Model aircraft are flying or non flying models of existing or imaginary aircraft using a variety of materials including plastic, diecast metal, polystyrene, balsa wood, foam and fibreglass. Flying designs range… … Wikipedia
Time travel — This article details time travel itself. For other uses, see Time Traveler. Time travel is the concept of moving between different moments in time in a manner analogous to moving between different points in space, either sending objects (or in… … Wikipedia
model — 01. She worked as a [model] in Milan for a couple of years, and then went into fashion design herself. 02. My son and I enjoy playing with his [model] rockets on the weekends. 03. The boys raced their [model] cars across the school field. 04.… … Grammatical examples in English
New Zealand's Next Top Model, Cycle 2 — New Zealand s Next Top Model Cycle 2 Promotional photograph of the cast of Cycle 2 of New Zealand s Next Top Model Format Reality television Created by Tyr … Wikipedia
New Zealand's Next Top Model, Cycle 3 — New Zealand s Next Top Model Cycle 3 Promotional photograph of the cast of Cycle 3 of New Zealand s Next Top Model Format Reality television Created by Tyr … Wikipedia
List of onetime The Simpsons characters — Further information: List of characters in The Simpsons and List of recurring characters in The Simpsons The following is a list of one time characters from the American animated television comedy series The Simpsons. Some of the… … Wikipedia
List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… … Wikipedia
List of mathematics articles (F) — NOTOC F F₄ F algebra F coalgebra F distribution F divergence Fσ set F space F test F theory F. and M. Riesz theorem F1 Score Faà di Bruno s formula Face (geometry) Face configuration Face diagonal Facet (mathematics) Facetting… … Wikipedia
Markov chain — A simple two state Markov chain. A Markov chain, named for Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized … Wikipedia
List of One Tree Hill characters — The original five from the first season; Upper row (L R) Lucas, Peyton and Haley. Lower row (L R) Brooke and Nathan. One Tree Hill is an American television series created by Mark Schwahn for The WB in 2003. After its third season, The WB and UPN … Wikipedia