Blurb::

Computes the double sided tolerance interval equivalent normal distribuion.

Description::

The "tolerance_intervals" keyword is used to compute (i) the equivalent
normal distribution, given response samples and a desired conficence level
between 0 and 1, and (ii) the lower and upper ends of an inverval covering
the samples, given a desired coverage between 0 and 1 :cite:p:`Jekel20`.

*Default Behavior*

By default, coverage is set to 0.95 (95%) and confidence level is set to 0.90 (90%).

*Expected Output*

Dakota first analyzes the N response samples supplied by the user, and
eliminates any sample with a NAN value, resulting in a final amount
M <= N of samples to be actually used in the calculations. If M >= 2,
then Dakota computes 6 values: the sample mean 'mu', the sample standard
deviation 's', the multiplicative factor 'f', the tolerance interval
lower end 'mu-f*s', the tolerance interval upper end 'mu+f*s', and the
standard deviation 's_equiv' of the tolerance interval equivalent normal.

Topics::

Examples::

.. code-block::

    method
      sampling
        samples 5
        refinement_samples 4 3 3
        sample_type random
        tolerance_intervals
          coverage 0.96
          confidence_level 0.92
        seed = 31415

Theory::

Faq::

See_Also::
