WebCab Probability and Statistics for .NET v3.3 Demo

ContinuousProbabilityDistributionApproximation Class

Within this class we offer methods which quantitatively access how well a given probability distribution approximates a given data set.

For a list of all members of this type, see ContinuousProbabilityDistributionApproximation Members.

System.Object
   ContinuousProbabilityDistributionApproximation

public class ContinuousProbabilityDistributionApproximation

Remarks

In particular, we evaluate the squared error for approximating a given distribution (i.e. data set with corresponding midpoints and frequencies for each of the intervals in which the range is subdivided into) by a standard continuous probability distribution.

Further Explanation

In order to access to what degree a given data set can be modeled by a given (continuous) distribution we introduce the squared errror measure of the approaximatiuon error. The spuared error is the sum of the squares of the distances between the frequency of the grouped data set (see details below) of the probability distribution at the midpoints of the grouped data set.

Groupded Data Sets

In order to assist in the analysis of a given data set it is often convenient (and in fact often nessesary) to collect the data into categories. For example, consider a data set which consists of the heights of a set of 100 people. Now in order to derive qualitative properties concerning this data set it is natural to group the data set into height intervals (i.e. such intervals could be 1.20m (or less), 1.21m - 1.50, 1.51- 2.00m, 2.01m (or more)). For each interval the number of members (i.e. frequency) of the original data set which fall within the interval would be recorded.

Remark A number of methods which can be applied in order to evaluated the mean, variance and standard deviation of grouped sets can be found in the Statictics GroupedData class of the Statistics :module:. Note that with this class the midpoint of each data class is treated as though it were the mean of all items in that class.

Requirements

Namespace: WebCab.Libraries.Statistics.PDistributions

Assembly: WebCab.Libraries.StatisticsDemo (in WebCab.Libraries.StatisticsDemo.dll)

See Also

ContinuousProbabilityDistributionApproximation Members | WebCab.Libraries.Statistics.PDistributions Namespace