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Lines Matching full:distribution

38 * [link math_toolkit.dist_ref.nmp.cdf_inv Inverse Cumulative Distribution Function].
63 [h4:cdf Cumulative Distribution Function]
66    RealType cdf(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist, const RealType& x);
73 the defined range for the distribution.
76 normal distribution:
80 [h4:ccdf Complement of the Cumulative Distribution Function]
82    template <class Distribution, class RealType>
83    RealType cdf(const ``['Unspecified-Complement-Type]``<Distribution, RealType>& comp);
93 the defined range for the distribution.
98    // standard normal distribution object:
104 normal distribution:
113    RealType hazard(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist, const RealType& x);
115 Returns the __hazard of /x/ and distribution /dist/.
118 the defined range for the distribution.
129    RealType chf(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist, const RealType& x);
131 Returns the __chf of /x/ and distribution /dist/.
134 the defined range for the distribution.
144    RealType mean(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
146 Returns the mean of the distribution /dist/.
148 This function may return a __domain_error if the distribution does not have
149 a defined mean (for example the Cauchy distribution).
154    RealType median(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
156 Returns the median of the distribution /dist/.
161    RealType mode(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
163 Returns the mode of the distribution /dist/.
165 This function may return a __domain_error if the distribution does not have
171    RealType pdf(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist, const RealType& x);
179 For a discrete distribution, the pdf is the probability that the
183 the defined range for the distribution.
185 For example, for a standard normal distribution the pdf looks like this:
192 … std::pair<RealType, RealType> range(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
194 Returns the valid range of the random variable over distribution /dist/.
199 …RealType quantile(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist, const RealType& p);
205 it is also the same as calculating the ['lower critical value] of a distribution.
212 distribution:
220    template <class Distribution, class RealType>
221    RealType quantile(const ``['Unspecified-Complement-Type]``<Distribution, RealType>& comp);
227    // define a standard normal distribution:
240 same as calculating the ['upper critical value] of a distribution.
247 distribution:
254    RealType standard_deviation(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
256 Returns the standard deviation of distribution /dist/.
258 This function may return a __domain_error if the distribution does not have
264 …std::pair<RealType, RealType> support(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist…
266 Returns the supported range of random variable over the distribution /dist/.
268 The distribution is said to be 'supported' over a range that is
278    RealType variance(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
280 Returns the variance of the distribution /dist/.
282 This function may return a __domain_error if the distribution does not have
288    RealType skewness(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
290 Returns the skewness of the distribution /dist/.
292 This function may return a __domain_error if the distribution does not have
298    RealType kurtosis(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
300 Returns the 'proper' kurtosis (normalized fourth moment) of the distribution /dist/.
304 Where [mu][sub i] is the i'th central moment of the distribution, and
305 in particular [mu][sub 2] is the variance of the distribution.
307 The kurtosis is a measure of the "peakedness" of a distribution.
320 of a normal distribution is zero.
322 This function may return a __domain_error if the distribution does not have
330    RealType kurtosis_excess(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
332 Returns the kurtosis excess of the distribution /dist/.
336 Where [mu][sub i] is the i'th central moment of the distribution, and
337 in particular [mu][sub 2] is the variance of the distribution.
339 The kurtosis excess is a measure of the "peakedness" of a distribution, and
341 the kurtosis excess of a normal distribution is zero.
343 This function may return a __domain_error if the distribution does not have
350 The kurtosis excess of a normal distribution is zero.
366 The inverse of the cumulative distribution function, is the same as the
385 given the area under the left tail of the distribution.
391 given the area under the right tail of the distribution.  It is equivalent to
401 The entropy (or differential entropy) of a continuous probability distribution /p/ is defined as