The distribution of the maximum of a first order moving average: the discrete case

Details The distribution of the maximum of a first order moving average: the discrete case The distribution of the maximum of a first order moving average: the discrete case

2008-02-04

arxiv.org/abs/0802.0529v3

Statistics

Methodology

13 pages. This version gives full solutions to the examples

Scientific paper

We give the distribution of $M_n$, the maximum of a sequence of $n$ observations from a moving average of order 1. Solutions are first given in terms of repeated integrals and then for the case where the underlying independent random variables are discrete. When the correlation is positive, $$ P(M_n \max^n_{i=1} X_i \leq x) = \sum_{j=1}^\infty \beta_{jx} \nu_{jx}^{n} \approx B_{x} r{1x}^{n} $$ where $\{\nu_{jx}\}$ are the eigenvalues of a certain matrix, $r_{1x}$ is the maximum magnitude of the eigenvalues, and $I$ depends on the number of possible values of the underlying random variables. The eigenvalues do not depend on $x$ only on its range.

Affiliated with

Also associated with

No associations

Rating

The distribution of the maximum of a first order moving average: the discrete case does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The distribution of the maximum of a first order moving average: the discrete case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The distribution of the maximum of a first order moving average: the discrete case will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-45239