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