Algorithm: Statistics functions


Functions
template<typename InputIterator>
std::iterator_traits< InputIterator >::value_type	ads::computeMinimum (InputIterator beginning, InputIterator end)
	Compute the minimum value for the elements in the range.
template<typename InputIterator>
std::iterator_traits< InputIterator >::value_type	ads::computeMaximum (InputIterator beginning, InputIterator end)
	Compute the maximum value for the elements in the range.
template<typename InputIterator, typename T>
void	ads::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	ads::computeMean (InputIterator beginning, InputIterator end)
	Compute the mean value for the elements in the range.
template<typename InputIterator, typename T>
void	ads::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	ads::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	ads::computeVariance (ForwardIterator beginning, ForwardIterator end)
	Compute the variance for the elements in the range.
template<typename ForwardIterator, typename T>
void	ads::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.

Function Documentation

template<typename ForwardIterator, typename T>

void ads::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.

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 ads::computeMeanAndVariance	(	ForwardIterator	beginning,
		ForwardIterator	end,
		T *	mean,
		T *	variance
	)

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.

Generated on Fri Aug 24 12:55:37 2007 for Algorithms and Data Structures Package by

1.4.7

Algorithm: Statistics functions

Functions

Function Documentation