OpenTURNS
Wilks¶
- class Wilks(*args)¶
Class to estimate a confidence interval on a quantile.
Refer to Estimation of a quantile upper bound by Wilks’ method.
- Parameters:
- X
RandomVector, A random vector of dimension 1.
- X
Methods
ComputeSampleSize(quantileLevel, confidenceLevel)Evaluate the minimum size of the sample.
computeQuantileBound(quantileLevel, ...[, ...])Evaluate an upper bound of a quantile.
Notes
This static class estimates an upper bound of the quantile of level
![\alpha \in [0,1]](data:image/svg+xml;base64,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)
of the random variable 
with a confidence greater than 
, using a given order statistics.Let
be the unknown quantile of level 
of the random variable of dimension 1.
Let 
be a sample of independent and identically distributed variables according to .
Let 
be the 
-th order statistics of which means that
is the -th maximum of for 
.
For example, 
is the minimum
and 
is the maximum. We have:
Given
, and 
, the class estimates the minimal size 
such that:
Once the minimal size
has been estimated, a sample of size can be generated from
and an upper bound of is estimated by the value of the 
on the sample.- __init__(*args)¶
- static ComputeSampleSize(quantileLevel, confidenceLevel, marginIndex=0)¶
Evaluate the minimum size of the sample.
- Parameters:
- alphapositive float in
The level
of the quantile.- betapositive float in ,
The confidence level on the upper bound.
- iint
The index such that
is an upper bound of
with confidence .
Default value is 
.
- alphapositive float in
- Returns:
- nint,
The minimum size of the sample.
Notes
The minimum sample size
is such that:
- computeQuantileBound(quantileLevel, confidenceLevel, marginIndex=0)¶
Evaluate an upper bound of a quantile.
- Parameters:
- alphapositive float in
The level
of the quantile.- betapositive float in
The confidence level on the upper bound.
- iint
The index such that
is an upper bound of
with confidence level .
Default value is .
- alphapositive float in
- Returns:
- upperBound
Point The estimate of the quantile upper bound.
- upperBound
Notes
The method starts by evaluating the minimum sample size
such that:Then, it generates a sample of size
from the random vector . The upper bound of
is 
, that is, the 
-th observation in the ordered sample.
