Computes statistics for mean and variance inferences using a sample from a normal population.

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

Syntax

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

Remarks

The statistics for mean and variance inferences are computed by using a sample from a normal population, including methods for the confidence intervals and tests for both mean and variance. The definitions of mean and variance are given below. The summation in each case is over the set of valid observations, based on the presence of missing values in the data.

Property Mean, returns value

\bar x = \frac{{\sum {x_i } }}{n}

\Delta _s^d Z_t

Property StdDev, returns value

s = \sqrt {\frac{{\sum {\left( {x_i - \bar x} \right)^2 } }}{{n - 1}}}

The property TTest returns the t statistic for the two-sided test concerning the population mean which is given by

t = \frac{{\bar x - \mu _0 }}{{s/\sqrt n }}

where s and \bar x are given above. This quantity has a T distribution with n - 1 degrees of freedom. The property TTestDF returns the degree of freedom.

Property ChiSquaredTest returns the chi-squared statistic for the two-sided test concerning the population variance which is given by

\chi ^2 = \frac{{\left( {n - 1} \right)s^2 }}{{\sigma _0^2 }}

where s is given above. This quantity has a \chi ^2 distribution with n - 1 degrees of freedom. Property ChiSquaredTestDF returns the degrees of freedom.

Inheritance Hierarchy

System..::.Object
Imsl.Stat..::.NormOneSample

See Also