NormOneSample Class

NormOneSample Class

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

Inheritance Hierarchy

SystemObject
Imsl.StatNormOneSample

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

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[SerializableAttribute]
public class NormOneSample

<SerializableAttribute>
Public Class NormOneSample

[SerializableAttribute]
public ref class NormOneSample

[<SerializableAttribute>]
type NormOneSample =  class end

The NormOneSample type exposes the following members.

Constructors

	Name	Description
	NormOneSample	Constructor to compute statistics for mean and variance inferences using a sample from a normal population.

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Methods

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Properties

	Name	Description
	ChiSquaredTest	Returns the test statistic associated with the chi-squared test for variances.
	ChiSquaredTestDF	Returns the degrees of freedom associated with the chi-squared test for variances.
	ChiSquaredTestNull	The null hypothesis value for the chi-squared test.
	ChiSquaredTestP	Returns the probability of a larger chi-squared associated with the chi-squared test for variances.
	ConfidenceMean	The confidence level (in percent) for a two-sided interval estimate of the mean.
	ConfidenceVariance	The confidence level (in percent) for two-sided interval estimate of the variances.
	LowerCIMean	Returns the lower confidence limit for the mean.
	LowerCIVariance	Returns the lower confidence limits for the variance.
	Mean	Returns the mean of the sample.
	StdDev	Returns the standard deviation of the sample.
	TTest	Returns the test statistic associated with the t test.
	TTestDF	Returns the degrees of freedom associated with the t test for the mean.
	TTestNull	Sets the Null hypothesis value for t test for the mean.
	TTestP	Returns the probability associated with the t test of a larger t in absolute value.
	UpperCIMean	Returns the upper confidence limit for the mean.
	UpperCIVariance	Returns the upper confidence limits for the variance.

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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.

Reference

Imsl.Stat Namespace

Other Resources

Example