CodeCogs

Calculates the statistics for a set of data that may change size frequently.

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Interface

#include <codecogs/statistics/moments/statistics.h>

using namespace Statistics::Moments;

Statistics() : m_n(size), m_calc(false), m_total(0), m_total1(0), m_total2(0), m_total3(0), m_total4(0), m_prod(1)
Statistics(int size, T *data)
void add(T x)
void calcStats()
void print()
inline double getTotal()
inline double getMean()
inline double getGeometricMean()
inline double getHarmonicMean()
inline double getVariance()
inline double getStdev()
inline double getSkewness()
inline double getKurtosis()
inline double getCV()
inline int getSize()
Statistics& operator+(const Statistics &B)

Overview

This class allows the calculation of key statistics for a set of data that may change its size frequently. The main advantage of this class is the ability of updating the key statistics while storing minimum information about previous data into a set of main variables given below, rather than storing the actual data. Based on the next main variables, that are recalculated with each new value that is added to the population,

$S=\sum_{i=1}^N x_i \qquad S_1=\sum_{i=1}^N \frac{1}{x_i} \qquad S_2=\sum_{i=1}^N x_i^2 \f] \f[ S_3=\sum_{i=1}^N x_i^3 \qquad S_4=\sum_{i=1}^N x_i^4 \qquad prod=\prod_{i=1}^N x_i$

(1)

it calculates the statistics using the following formulas

$mean=\frac{S}{N}\f] \f[geomean=\sqrt[N]{prod}\f] \f[harmean=\frac{N}{S_1}\f] \f[var=\frac{S_2-2\overline{x}S+N\overline{x}^2}{N-1}\f] \f[stdev=\sqrt{var}$

(2)

where mean is the arithmetic mean, geomean is the geometric mean, harmean is the harmonic mean,var </em> is the variance and stdev is the standard deviation. The skewness and kurtosis are calculated using similar formulas.

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References

http://office.microsoft.com/en-us/FX010858001033.aspx

Example 1

#include <codecogs/statistics/moments/statistics.h>
    #include <iostream>
    int main()
    {
      double a[15];
      for (int i = 0; i < 15; i++)
        a[i]=i+1;
      a[1]=5;
      Stats::Moments::Statistics<double> stats(15, a);
      stats.print();
      return 0;
    }

Output:

Total = 123.0000000000
    Arithmetic Mean = 8.2000000000
     Geometric Mean = 6.8280387111
      Harmonic Mean = 4.9698018386
           Variance = 18.0285714286
 Standard Deviation = 4.2460065271
           Skewness = 0.0403100873
           Kurtosis = -1.0487842858

Members of Statistics

CLASS METHOD

Statistics

Default constructor which resets all variables

CLASS METHOD

Statistics

This constructor takes an array as input, which is analyzes to compute the various statistical parameters

Parameters

data

A pointer to the data array

size

The number of elements within the data array to analyze

CLASS METHOD

add

This function adds a new value to the statistical collection. Additional values are appended in constant time very quickly, enabling you to call this function thousands of times in quick succession with no penalty.

Parameters

value to be added to the accumulating statistics

CLASS METHOD

calcStats

One this class is loaded with the values that you want analysed, this function must be run to compute the final values such as mean, variance etc. This function need only be run once before all statistics can be retrieved.

CLASS METHOD

print

Calculates and prints the key statistics of the current population.

CLASS METHOD

getTotal

$total = \sum_{i=1}^N x_i$

(3)

CLASS METHOD

getMean

$\overline{x} = \frac{1}{N} \sum_{i=1}^N x_i$

(4)

CLASS METHOD

getGeometricMean

$geom=\sqrt[N] {\prod_{i=1}^N x_i}$

(5)

CLASS METHOD

getHarmonicMean

$harm=\frac{N}{\sum_{i=1}^N\frac{1}{x_i}}$

(6)

CLASS METHOD

getVariance

$var=\frac{1}{N-1}\sum_{i=1}^N(x_i-\overline{x})^2$

(7)

CLASS METHOD

getStdev

$\sigma = \sqrt{ \frac {1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2 }$

(8)

CLASS METHOD

getSkewness

$skew= \frac{N}{(N-1)(N-2) \sigma^3} \sum_{i=1}^N (x_i - \overline{x})^3$

(9)

CLASS METHOD

getKurtosis

$kurt= \frac{1}{(N-2)(N-3)}\left( \frac{N(N+1)}{(N-1) \sigma^4} \sum_{i=1}^N (x_i - \overline{x})^4 - 3(N-1)^2 \right)$

(10)

CLASS METHOD

getCV

$CV= \frac{\sigma}{\overline{x}}$

(11)

CLASS METHOD

getSize

Calculates the size of the set of data.

CLASS METHOD

operator+

Combines the statistics from two independent Statistics objects. This is equivalent to having added all the data to just one container, with all the statistical measures maintained accurately. i.e

Stats::Moments::Statistics<double> A(15, somearray_a);
  Stats::Moments::Statistics<double> B(51, somearray_b);

  //This contains the combined statistics 
  Stats::Moments::Statistics<double> C = A+B;

Parameters

the Statistics container to add to the current object