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Java FTP Component
Java Secure FTP, FTP, SSL, SSH
Java SSH, Java Telnet
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SSH .NET
FTP .NET, FTPS .NET
Java FTP
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| Classes / Algorithms / WebCab Probability and Statistics (J2EE Edition) |
This suite consists of five packages: Statistics, Discrete Probability,
Standard Probability Distributions, Hypothesis Testing, and Correlation &
Regression which offer the following functionality.
Statistics Module
The Statistics module incorporates evaluation procedures of standard
quantitative measures of centrality (mean) and dispersion of (discrete)
numerical sets. This module incorporates
weighted averages, geometric mean, Inter-Quartile range, mean and standard
deviation, sample variance and the coefficient of variation.
Discrete Probability Module
The Discrete Probability module encapsulates the foundations of discrete
probability and discrete probability distributions. This component includes
the addition law, conditional probability, cumulative distribution function,
mean and variance of a distribution, expected values, covariance and
simplification of expressions involving random variables.
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. We cover
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 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.
Confidence Intervals and Hypothesis Testing Module
Within this component we present 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.
Product Details
This suite consists of four modules with the following features:
Statistics Module
- Measures of Mean
- Arithmetic Mean - a measure of centrality for quantitative data.
- Median - the middle value when the observations are arranged
in order of 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 numerical
observations.
- Range - the difference between the largest and the smallest
observation.
- Measures of Dispersion
- Inter-Quartile Range (IRQ) - a measure of dispersion which is
not affected by extreme values.
- Mean Deviation - the sum of the distances between the
observation and the arithmetic mean.
- Sample Variance - the sum of the squares of the distances
between the observations and the
arithmetic mean.
- Sample Standard Deviation - the measure of dispersion which
has the same units as the observations and is the square root of the sample variance.
- Coefficient of Variation - computes the spread of sets for
observations which have been made in different units.
- Data Presentation
- Frequency Tables - show the number of the elements inside
some intervals.
- Cumulative Frequency Tables - show the number of the elements
within a data set either the highest value (or above the lowest value) of
the present frequency table.
- Relative Frequency Tables - help to compare two or more data
sets, normalized the frequencies.
Discrete Probability Module
- Discrete Probability
- Discrete probability - a priori and relative frequency definition.
- The Addition Law - used when combining event set or testing for their independence.
- Conditional probability - the probability of an event assume that another event takes place.
- Complementary event probability - the probability of a set of events not taking place.
- Discrete Probability Distributions
- Cumulative distribution function - the sum of the probabilities of a sequence of events.
- Mean - the sum of the product of the probability of an event with its value.
- Variance - a measure of the distributions spread from the mean.
- Expected values - the expected value of the random variable.
- Covariance - the covariance of two random variables.
- Ro - the population correlation coefficient of two random variables.
- Expression with random variables and basic probability laws
- Simplify expression - simplify expressions involving the mean, variance,
expected values and covariance of random variables.
- Union and Intersection - the basic formulae for calculating the union and the
intersection of two or many events.
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.
- 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 contains the following features:
- GUI Bundle - we bundle a suite of graphical user interface
JavaBean components (with 1, 2, 4 or site-wide license) allowing the
developer to plug-in a wide range of GUI functionality (including
charts/graphs) into their client applications
- EAR Files - we provide individual customized EAR files for
the most widely used application servers including IBM WebSphere 4.0/5.0,
BEA WebLogic 6.1/7.0, Oracle 9iAS, Sun ONE AppServer 7, Ironflare Orion
1.5.2/1.6.0, Borland AppServer 5.0, Sybase EAServer 3.6 and JBoss 2.4.4/3.0.0
- Self-Deploy - the relevant servers EAR file will be self-deployed
onto supported local application servers during the installation of the
self-install package. The supported application servers include IBM WebSphere
4.0/5.0, BEA WebLogic 6.1/7.0, Oracle 9iAS, Borland AppServer 5.0, Ironflare
Orion 1.5.2/1.6.0 and JBoss 2.4.4/3.0.0
- UML Models - to assist system architects we provide UML
diagrams of this component
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