eldo_user

Stopping Test for AVG
Monte Carlo Analysis
CONFIDENCE Technique
Suppose it is required to estimate μ with a random sequence θ 1 , θ 2 , ..., θ n whose distribution
depends on μ. Then L(Y) and U(Y) are searched for such that:
where 0 ≤ α ≤ 1 is a pre-specified number. We then say that [L(θ), U(θ)] is a 100(1 − α)%
confidence interval for μ.
There are two types of error to consider:
• The absolute error, given by:
• The relative error, given by:
It is known that as so that the errors both tend to 0. If μ = 0 then the relative
error E r is not defined. The following error criterion is specified:
Error Criterion: Given 0 ≤ α ≤ 1 and ε > 0, the condition required is:
E is the error type specified (relative or absolute).
To satisfy the condition
, then samples continue to be generated until:
where z 1 −α/2 is the (1 −α/2) percentile point of the N(0, 1) distribution and σ p is the estimate of
σ based upon the first p samples. It is important that p be sufficiently large, so that μ n and σ n are
sufficiently good estimates of μ and σ respectively. As a result, it is typically insisted that p = 20
before stopping. The parameter p may be redefined by setting the NRUN_PILOT within the
MCCONV function.
Eldo® User's Manual, 15.3 515