Computes basic univariate statistics.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
[SerializableAttribute]
public class Summary
Visual Basic (Declaration)
<SerializableAttribute> _
Public Class Summary
Visual C++
[SerializableAttribute]
public ref class Summary

Remarks

For the data in x, Summary computes the sample mean, variance, minimum, maximum, and other basic statistics. It also computes confidence intervals for the mean and variance if the sample is assumed to be from a normal population.

Missing values, that is, values equal to NaN (not a number), are excluded from the computations. The sum of the weights is used only in computing the mean (of course, then the weighted mean is used in computing the central moments). The definitions of some of the statistics are given below in terms of a single variable x. The i-th datum is x_i, with corresponding weight w_i. If weights are not specified, the w_i are identically one. The summation in each case is over the set of valid observations, based on the presence of missing values in the data.

Number of nonmissing observations,

n = \sum {f_i }

Mean,

\bar x_w = \frac{{\sum {f_i w_i x_i } }}{{\sum {f_i w_i } }}

Variance,

s_w^2 = \frac{{\sum {f_i w_i \left( {x_i - \bar x_w } \right)^2 } }}{{n - 1}}

Skewness,

\frac{{\sum {f_i w_i \left( {x_i - \bar x_w } \right)^3 /n} }}{{[\sum {f_i w_i \left( {x_i - \bar x_w } \right)^2 /n]^{3/2} } }}

Excess or Kurtosis,

\frac{{\sum {f_i w_i \left( {x_i - \bar x_w } \right)^4 /n} }}{{[\sum {f_i w_i \left( {x_i - \bar x_w } \right)^2 /n]^2 } }} - 3

Minimum,

x_{\rm min} = \min (x_i )

Maximum,

x_{\rm max} = \max (x_i )

Inheritance Hierarchy

System..::.Object
Imsl.Stat..::.Summary

See Also