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# WebCab Probability and Stat for .NET 3.6

## WebCab Probability and Stat for .NET 3.6

### WebCab Probability and Stat for .NET 3.6 Ranking & Summary

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File size: 5.9 Mb
Platform: Windows
Price: \$179.00
Publisher: WebCab Components

### WebCab Probability and Stat for .NET 3.6 description

WebCab Probability and Stat for .NET 3.6 is a suite including six packages: Statistics, Discrete Probability, Standard Probability Distributions, Curve Fitting, Hypothesis Testing, and Correlation & Regression which have the following functionality:

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), Grouped Data (incl. Sample Mean, Variance and Standard Deviation) and Quality Control(incl. R-Chart, S-Chart and Median Chart).

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.

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. We also offer methods which randomly generate numbers from a given distribution.

Curve Fitting

Allows the fitting of linear and non-linear functions for a data set which may or may not exhibit measurement errors in accordance with the least squares approach. A general linear algorithm and the specialized Levenberg-Marquardt algorithm to handle the non-linear case are provided.

Confidence Intervals and Hypothesis Testing Module

Within this component this program includes two aspects of inferential statistics known as confidence intervals and hypothesis testing. 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.

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.

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 our .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 - It can provide 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 - use a ASP.NET service to perform component calculations on SQL database columns from a remote DBMS. This program can apply 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.

Major Features:

1. 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.
• Skewness - Measures the symmetry of the data set considered.
• Kurtosis - Measures of whether the data set is peaked or flat realtive to the normal distribution.
• Maximum - Finds the maximum of the data set.
• Minimum - Finds the minimum of the data set.
• 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.
• Quality Control
• R-Chart - Calculate the control limits (RBAR, LCL, UCL) for the R-Chart.
• S-Chart - Calculate the control limits (SBAR, LCL, UCL) for the S-Chart.
• Median Chart - Calculate the control limits for the Median Chart.
2. 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.
3. 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.
4. 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.
5. Curve Fitting
• Linear Curve Fitting - Allows the fitting in accordance with the least square approach of linear functions to a data set which may or may not exhibit measurement errors.
• General Linear Algorithm - Fits all linear functions which can be provided by implementing our function interface or via the Linear Factor model function builder.
• Linear Factor Model function builder - Allows a linear function to be constructed by a iterative sequence of method calls.
• Analysis of Variance (ANOVA) - Residuals, SSE, MSE, SST, SSR, MSR, Standard Error, R-Squared, Adjusted R-Squared, F-test.
• Line With Error - Fits a straight line to a set of experimental data with(out) errors.
• Trend Line Polynomial - Static procedures for the fitting any polynomial function to a data set which may or may not exhibit errors.
• Analytic Fitting - Fits a power function, logarithm function or exponential function to a given data set.
• Non-Linear Curve Fitting - Allows the fitting of non-linear functions to given data set.
• Levenberg - Marquardt algorithm - Fits a non-linear function which is provided by either implementing our non-linear function interface or via our Non-Linear Factor model function builder.
• Non-Linear Factor Model Function Builder - Allows a non-linear function to be constructed by a iterative sequence of method calls.
• Analysis of Variance (ANOVA) - Residuals, SSE, MSE, SST, SSR, MSR, Standard Error, R-Squared.
6. 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.

Requirements:

1. Prerequisites and Compatibility Requirements:
• Pentium IIĀ® 500Mhz
• 64MB RAM
• .NET Framework v1.x
2. Compatibility Operating System for Deployment:
• Windows Server 2003, 2000
• Windows XP Professional
3. Software Requirements:
• .NET Framework v1.0 (or higher)
4. Built Using:
• .NET Framework v1.0
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