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- [section:dist_algorithms Distribution Algorithms]
- [h4 Finding the Location and Scale for Normal and similar distributions]
- Two functions aid finding location and scale of random variable z
- to give probability p (given a scale or location).
- Only applies to distributions like normal, lognormal, extreme value, Cauchy, (and symmetrical triangular),
- that have scale and location properties.
- These functions are useful to predict the mean and/or standard deviation that will be needed to meet a specified minimum weight or maximum dose.
- Complement versions are also provided, both with explicit and implicit (default) policy.
- using boost::math::policies::policy; // May be needed by users defining their own policies.
- using boost::math::complement; // Will be needed by users who want to use complements.
- [h4 find_location function]
- ``#include <boost/math/distributions/find_location.hpp>``
- namespace boost{ namespace math{
- template <class Dist, class ``__Policy``> // explicit error handling policy
- typename Dist::value_type find_location( // For example, normal mean.
- typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
- // For example, a nominal minimum acceptable z, so that p * 100 % are > z
- typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
- typename Dist::value_type scale, // scale parameter, for example, normal standard deviation.
- const ``__Policy``& pol);
- template <class Dist> // with default policy.
- typename Dist::value_type find_location( // For example, normal mean.
- typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
- // For example, a nominal minimum acceptable z, so that p * 100 % are > z
- typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
- typename Dist::value_type scale); // scale parameter, for example, normal standard deviation.
- }} // namespaces
- [h4 find_scale function]
- ``#include <boost/math/distributions/find_scale.hpp>``
- namespace boost{ namespace math{
- template <class Dist, class ``__Policy``>
- typename Dist::value_type find_scale( // For example, normal mean.
- typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
- // For example, a nominal minimum acceptable weight z, so that p * 100 % are > z
- typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
- typename Dist::value_type location, // location parameter, for example, normal distribution mean.
- const ``__Policy``& pol);
- template <class Dist> // with default policy.
- typename Dist::value_type find_scale( // For example, normal mean.
- typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
- // For example, a nominal minimum acceptable z, so that p * 100 % are > z
- typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
- typename Dist::value_type location) // location parameter, for example, normal distribution mean.
- }} // namespaces
-
- All argument must be finite, otherwise __domain_error is called.
- Probability arguments must be [0, 1], otherwise __domain_error is called.
- If the choice of arguments would give a negative scale, __domain_error is called, unless the policy is to ignore, when the negative (impossible) value of scale is returned.
-
- [link math_toolkit.stat_tut.weg.find_eg Find Mean and standard deviation examples]
- gives simple examples of use of both find_scale and find_location, and a longer example finding means and standard deviations of normally distributed weights to meet a specification.
- [endsect] [/section:dist_algorithms dist_algorithms]
- [/ dist_algorithms.qbk
- Copyright 2007 John Maddock and Paul A. Bristow.
- Distributed under the Boost Software License, Version 1.0.
- (See accompanying file LICENSE_1_0.txt or copy at
- http://www.boost.org/LICENSE_1_0.txt).
- ]
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