# WebCab Probability and Statistics for .NET - Summary

by WebCab - Product Type: Component / .NET Web Service / 100% Managed Code / ActiveX DLL

## Summary

WebCab Probability and Statistics for .NET by WebCab

URLs: webcab-probability-statistics-net, webcab probability statistics net, webcabprobabilitystatisticsnet, webcab

Add Statistics, Discrete Probability, Standard Probability Distributions, Hypothesis Testing, Correlation and Linear Regression functionality to your .NET, COM, and XML Web service Applications. WebCab Probability and Statistics for .NET consists of 5 main modules. The Statistics module incorporates evaluation procedures of standard quantitative measures of centrality (mean) and dispersion of (discrete) numerical sets. The Discrete Probability module encapsulates the foundations of discrete probability and discrete probability distributions. The Standard Probability Distributions Module assists in the development of server-side applications that incorporate the Binomial, Poisson, Normal, Lognormal and Pareto probability distributions. The Confidence Intervals and Hypothesis Testing Module presents two aspects of inferential statistics known as confidence intervals and hypothesis testing.

Statistics Module

The Statistics module incorporates topic from data presentation (incl. standard, relative and cumulative frequency tables), Basic Statistics (incl. measure of centrality, dispersion and relative location) and Grouped Data (incl. Sample Mean, Variance and Standard Deviation).

Discrete Probability Module

The Discrete Probability module encapsulates the probabilistic study of finite set of events (i.e. discrete probability) and experiments with a finite number of outcomes (i.e. discrete random variables). Including: probability measures, union/intersection law, conditionals/complementary probability; cumulative distribution functions, mean/variance/expected return of Random Variable.

Correlation and Regression Module

Allows the user to investigate relationships between two variables. These finding can be used to predict one variable from the given values of other variables. Covered are linear (Spearman's, t-test, z-transform) and rank (Spearman's, Kendall's) correlation, linear regression and conditional means.

Standard Probability Distributions Module

This module assists in the development of applications that incorporate the Binomial, Poisson, Normal, Lognormal, Pareto, Uniform, Hypergeometric, Weibull and Exponential probability distributions. The probability density function, cumulative distribution function and inverse, mean, variance, Skewness and Kurtosis are implemented where appropriate and/or their approximations for each distribution. Also offered are methods which randomly generate numbers from a given distribution.

Confidence Intervals and Hypothesis Testing Module

Within this component two aspects of inferential statistics known as confidence intervals and hypothesis testing are presented. Confidence intervals determine the level of confidence in pointwise statistics (e.g. mean, variance) of the sample in relation to the statistics for the entire population. With hypothesis testing the user can judge which of several hypotheses sampled evidence best supports.

This suite offers the following functionality:

Statistics Module

Data Presentation

Frequency Tables - Evaluate the Frequency table with respect to open left or open right boundary convention.

Cumulative Frequency Tables - Evaluate the Cumulate Frequency from above or below with respect to the open left or open right boundary convention.

Relative Frequency Tables - Evaluate the Normalized (or Relative) Frequency Table from above or below with respect to the open left or open right boundary convention.

Measures of Centrality

Arithmetic Mean - a measure of centrality for quantitative data.

Median - the middle value when the observations have be ordered by magnitude

Mode - the most frequently occurring observation.

Weighted Average - the arithmetic average of a weighted set

Geometric Mean - the nth root of the product of all n numerical observations.

Measures of Dispersion

Range - the difference between the largest and smallest observations.

Inter-Quartile Range (IRQ) - a measure of dispersion which is not affected by extreme values.

Mean Deviation - Evaluates the average difference between the mean of the observations.

Sample Variance - The variance from the mean of a Sample of observations.

Sample Standard Deviation - Square root of the Sample Variance which has the same units as the observations.

Coefficient of Variation - Relative value of the Standard deviation with regard to the mean.

Measures of Relative Location

Percentile - The i-th percentile of a data set is the value such that at least i percent of the data set items are less than or equal to this value.

z-Score - Evaluates the number of standard deviations of a given element of the data set is from the mean.

Chebyshev's Theorem - Calculate the percentage of items that must be within a specified number of standard deviations from the mean.

Grouped Data

Sample Mean - Calculate the mean of a sample of grouped data.

Sample Variance - Evaluate the variance of a sample of grouped data.

Samples Standard Deviation - Evaluate the standard deviation of a sample of grouped data.

Discrete Probability Module

Random Variables

Set/Get Random Variable - Set (and get) a Random Variable to an internal tables of random variables.

Associated Probability Distribution - Evaluation of the Probability Distribution associated to the Random Variable considered.

Cumulative distribution function - of a Random Variable set or passed via parameters.

Variance - the variance of a random variable from the internal table or passed via parameters.

Expected value - the expected value of the random variable from the interval table or passed via parameters.

Discrete Probability

Set Probability Measure - Set (and get) the probability measure on a discrete set.

Calculate Probability - Calculates the probability of a number of independent events.

Union - Calculates the probability of one event occurring from two collections of events.

Intersection - Calculates the probability of the intersection of two sets of events occurring.

Conditional Probability - Evaluates the probability of an event assuming that another event takes place.

Complementary Probability - Evaluate the probability of a set of events not taking place.

Correlation and Regression Module

Statistic quantities

Mean - calculates the arithmetic mean.

Sample variance - calculates the sample variance.

Correlation coefficients

Pearson's product moment correlation coefficient - the most widely used linear correlation coefficient for a data set.

t-test, z-transform - provides an analytic framework to establishing a confidence level for Pearson's coefficient.

Spearman's and Kendall's rank correlation coefficients - measure the association between two variables of an ordered data set.

Regression line - using the method of least squares to determine the line of best fit.

Confidence interval for the conditional mean - determines the confidence interval for the true regression line.

Standard Probability Distributions Module

Discrete Random Variables

Binomial distribution - used to model an experiment which has two outcomes `successes' and `failures' of elements from a finite set.

Poisson distribution - used to model instances such as the number of cars arriving at a petrol station over 1 hour.

Poisson Approximation of the Binomial distribution - Approximation of the Binomial distribution used when the number of trial is large and the probability of is small.

Hypergeometic Probability Distribution - closely related to the Binomial probability distribution.

Normal Approximation of the Binomial Distribution - approximation of the Binomial Probability Distribution by the Normal Probability Distribution.

Continuous Random Variables

Normal distribution - Used in a broad range of applications include finance (asset price evolution,...), scientific measurement,...

Log Normal distribution - Used for example when modeling investment returns and the distribution of insurance claim sizes.

Pareto Distribution - Useful for cautiously modeling the distribution of large insurance claims.

Uniform Distribution - Used to model situations where the probability is proportional to the length of the interval.

Exponential Distribution - Can be used to describe situations such as the time between arrivals at a petrol station.

Weibull Distribution - Used within the study of the reliability of precision engineering parts.

Numerical Methods

Extended Trapezoidal Rule - this method is implemented in order to evaluate the non-analytic probability density functions of the Normal and Lognormal distributions.

Hypothesis Testing Module

Normal Confidence Interval - used when large samples with >30 elements are considered.

Two-sided confidence interval for the mean, proportions, difference between means and difference between proportions.

One-sided confidence interval for the mean, proportions and difference between means.

Estimating the sample size for a given confidence of the mean.

Estimating the sample size for a given confidence of the proportions.

Student Confidence Interval - used when small samples with <=30 elements are considered.

Two-sided confidence interval for the mean and the difference between means.

One-sided confidence interval for the mean.

Normal Hypothesis Testing - used when large samples with >30 elements are considered.

Two-sided hypothesis testing for the mean, proportions, difference between means and difference between proportions.

One-sided hypothesis testing for the mean, proportions, difference between means and difference between proportions.

Student Hypothesis Testing - used when small samples with <=30 elements are considered.

Two-sided hypothesis testing for the mean, proportions and the difference between means.

One-sided confidence interval for the mean, proportions and difference between means.

This product also has the following technology aspects:

3-in-1: .NET, COM, and XML Web services - Three DLLs, Three API Docs, Three Sets of Client Examples all in 1 product. Offering a 1st class .NET, COM, and XML Web service product implementation.

Extensive Client Examples - Multiple client examples including .NET (C#, VB.NET, C++.NET), COM and XML Web services (C#, VB.NET)

ADO Mediator - The ADO Mediator assists the .NET developer in writing DBMS enabled applications by transparently combining the financial and mathematical functionality of the .NET components with the ADO.NET Database Connectivity model.

Compatible Containers - Visual Studio 6 (incl. Visual Basic 6, Visual C++ 6), Visual Studio .NET (incl. Visual Basic .NET, Visual C#.NET, and Visual C++.NET), Borland's C++ Builder (incl. C++Builder, C++BuilderX, C++ 2005), Borland Delphi 3 - 2005, Office 97/2000/XP/2003.

ASP.NET Web Application Examples - An ASP.NET Web Application example which enables you to quickly test the functionality within this .NET Service.

ASP.NET Examples with Synthetic ADO.NET - An ASP.NET service to perform component calculations on SQL database columns from a remote DBMS. Applying a component's function to certain rows from the database and list the output in HTML format. This is a powerful feature since it allows you to perform calculations in a DBMS manner without having to code the C# to SQL database transaction yourself as it is all done by the ASP within the .NET Framework managed server side environment.

Add Statistics, Discrete Probability, Standard Probability Distributions, Hypothesis Testing, Correlation and Linear Regression functionality to your .NET, COM, and XML Web service Applications.

Pricing: WebCab Probability and Statistics for .NET V3.5 1 Developer License, WebCab Probability and Statistics for .NET V3.5 4 Developer Team License, WebCab Probability and Statistics for .NET V3.5 1 Site Wide License (Allows Unlimited Developers at a Single Physical Address)

Operating System for Deployment: Windows XP, Windows Server 2003, Windows 2000

Architecture of Product: 32Bit

Product Type: Component

Component Type: .NET Web Service, 100% Managed Code, ActiveX DLL

Web Services: SOAP Binding Style rpc

Built Using: Visual C# .NET

Compatible Containers: Microsoft Visual Studio .NET 2003, Microsoft Visual Studio .NET, Microsoft Visual Basic .NET 2003, Microsoft Visual Basic .NET, Microsoft Visual C++ .NET 2003, Microsoft Visual C++ .NET, Microsoft Visual C# .NET 2003, Microsoft Visual C# .NET, CodeGear C++ 5.0 (formerly Borland), CodeGear C++ (formerly Borland), C++Builder 6, C++Builder 5, C++Builder 4, C++Builder 3, Delphi 2005 (9.0), Delphi 8.0, C#Builder, .NET Framework 1.1, .NET Framework 1.0

Keywords: Math Stats Mathematics Mathematical Statistic Statistical

Part numbers: PC-514619-90569 514619-90569 PC-514619-90570 514619-90570 PC-514619-90571 514619-90571

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