Algorithm: Statistics functions

Functions
template<typename InputIterator >
std::iterator_traits < InputIterator >::value_type	computeMinimum (InputIterator beginning, InputIterator end)
	Compute the minimum value for the elements in the range.
template<typename InputIterator >
std::iterator_traits < InputIterator >::value_type	computeMaximum (InputIterator beginning, InputIterator end)
	Compute the maximum value for the elements in the range.
template<typename InputIterator , typename T >
void	computeMinimumAndMaximum (InputIterator beginning, InputIterator end, T minimum, T maximum)
	Compute the minimum and maximum values for the elements in the range.
template<typename InputIterator >
std::iterator_traits < InputIterator >::value_type	computeMean (InputIterator beginning, InputIterator end)
	Compute the mean value for the elements in the range.
template<typename InputIterator , typename T >
void	computeMinimumMaximumAndMean (InputIterator beginning, InputIterator end, T minimum, T maximum, T *mean)
	Compute the minimum, maximum, and mean for the elements in the range.
template<typename ForwardIterator , typename T >
void	computeMeanAndVariance (ForwardIterator beginning, ForwardIterator end, T mean, T variance)
	Compute the mean and variance for the elements in the range.
template<typename ForwardIterator >
std::iterator_traits < ForwardIterator > ::value_type	computeVariance (ForwardIterator beginning, ForwardIterator end)
	Compute the variance for the elements in the range.
template<typename ForwardIterator , typename T >
void	computeMeanAbsoluteDeviationVarianceSkewAndCurtosis (ForwardIterator beginning, ForwardIterator end, T mean, T absoluteDeviation, T variance, T skew, T *curtosis)
	Compute the mean, absolute deviation, variance, skew and curtosis for the elements in the range.

Detailed Description

Function Documentation

template<typename ForwardIterator , typename T >

void computeMeanAbsoluteDeviationVarianceSkewAndCurtosis	(	ForwardIterator	beginning,
		ForwardIterator	end,
		T *	mean,
		T *	absoluteDeviation,
		T *	variance,
		T *	skew,
		T *	curtosis
	)			`[inline]`

Compute the mean, absolute deviation, variance, skew and curtosis for the elements in the range.

To compute the variance, I use the corrected two-pass algorithm presented in "Numerical Recipes."

$\mathrm{variance}(x) = \frac{1}{N - 1} \left( \sum_{j = 0}^{N - 1} (x_j - \bar{x})^2 - \frac{1}{N} \left( \sum_{j = 0}^{N - 1} (x_j - \bar{x}) \right)^2 \right)$

Note that with exact arithmetic, the second sum is zero. With finite precision arithmetic, the term reduces the round-off error. The mean absolute deviation, skew, and curtosis are defined below.

$\mathrm{absoluteDeviation}(x) = \frac{1}{N} \sum_{j = 0}^{N - 1} |x_j - \bar{x}|$

$\mathrm{skew}(x) = \frac{1}{N \sigma^3} \sum_{j = 0}^{N - 1} (x_j - \bar{x})^3$

$\mathrm{curtosis}(x) = \left( \frac{1}{N \sigma^4} \sum_{j = 0}^{N - 1} (x_j - \bar{x})^4 \right) - 3$

Note that the skew and curtosis are not defined when the variance is zero. in this case, the function prints a warning.

template<typename ForwardIterator , typename T >

void computeMeanAndVariance	(	ForwardIterator	beginning,
		ForwardIterator	end,
		T *	mean,
		T *	variance
	)			`[inline]`

Compute the mean and variance for the elements in the range.

To compute the variance, I use the corrected two-pass algorithm presented in "Numerical Recipes."

$\mathrm{var}(x) = \frac{1}{N - 1} \left( \sum_{j = 0}^{N - 1} (x_j - \bar{x})^2 - \frac{1}{N} \left( \sum_{j = 0}^{N - 1} (x_j - \bar{x}) \right)^2 \right)$

Note that with exact arithmetic, the second sum is zero. With finite precision arithmetic, the term reduces the round-off error. CONTINUE.

Referenced by computeVariance().

Algorithm: Statistics functions

Functions

Detailed Description

Function Documentation