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SQLDistributions - Summary

by TotallySQL - Product Type: Component / .NET Class / 100% Managed Code

Summary

SQLDistributions by TotallySQL

URLs: sqldistributions, totallysql

Evaluation of PDF, CDF and their inverses; summary statistics; parameter estimation; high-volume random variate generation and much more. SQLDistributions extends and enhances your T-SQL programming environment by adding full-featured and highly accurate SQL implementations of 28 probability distributions. For each of these distributions the following functions are available: probability density function (pdf) and its inverse; cumulative density function (cdf) & its complement; quantile (inverse cdf) and its complement; hazard function; cumulative hazard function (chf), mean; median; mode; variance; standard deviation; skewness; kurtosis; percentile; percentilerank, flags: symmetric; unimodal; discontinuous (on left or right); strictly increasing / decreasing; inverted, minimum & maximum defined values for x; minimum & maximum supported values for x; minimum & maximum values of pdf, high-performance scalar and table-valued random variate generators (to generate random numbers that are distributed as per the distribution).

Easy to Use

All TotallySQL Transact-SQL extensions are implemented using familiar programming objects within SQL (scalar and table-valued functions, aggregate functions, user-defined types, stored procedures) , keeping the syntax clean and making them as fast and easy to use as the built-in native statistics functions. The distributions in SQLDistributions are all implemented as Types within SQL, so distributions can be instantiated and stored as single objects in tables and local variables.

Outstanding Performance and Numerical Accuracy

The algorithms behind the SQLDistributions use industry-proven, best-in-class techniques devised by some of the world's leading numerical computing experts to maximise performance and accuracy even for fairly extreme input values. Careful heuristics and edge-case checks through the code ensure that problems caused by the limitations of floating-point arithmetic on digital computers (such as cancellation errors) are kept to an absolute mininum, and a broad range of special-purpose, high-performance numerical computing approaches are used in place of the slow, expensive computations that would result from 'naive' implementations of the underlying mathematics. The random variate generators are blisteringly fast.

Supported Distributions

Continuous:

Beta

Cauchy

Chi-squared

Exponential

F

Gamma

Gumbel

Inverse chi-squared

Inverse gamma

Laplace

Logistic

Log-normal

Non-central beta

Non-central chi-squared

Non-central F

Non-central T

Normal

Pareto

Rayleigh

T

Triangular

Uniform

Weibull

Discrete

Bernouilli

Binomial

Hypergeometric

Negative binomial

Poisson

Functions Available (for all distributions)

Probability density function pdf(x)

Inverse probability density function - finds possible values of x for a given value of pdf(x)

Cumulative density function cdf(x) & its complement (for greater precision when cdf(x) is near 1)

Quantile (inverse of cdf) & its complement (for greater precision when input value p is near 1)

Hazard function & cumulative hazard function

Mean, mode, median, variance, standard deviation, skewness, kurtosis & kurtosis excess

Percentile & percentile rank

Flags: symmetric, unimodal, discontinuous (left & right), strictly increasing / decreasing, inverted

Minimum & maximum defined & supported values of x

Minimum & maximum values of pdf(x)

Scalar & table-valued random variate generator functions

Parameter accessors (allows distribution parameters to be read for stored distributions)

Distributions are implemented as types within SQL - they can be instantiated & stored in tables etc.

Constructor functions are provided for each distribution

Distributions can also be initialized / reset by assigning comma-separated parameter strings.

All functions exist as instance methods (object.method() syntax) and as static methods (type::method() syntax)

Evaluation of PDF, CDF and their inverses; summary statistics; parameter estimation; high-volume random variate generation and much more.

Operating System for Deployment: Windows 7, Windows Server 2008, Windows Server 2003

Architecture of Product: 32Bit, 64Bit

Product Type: Component

Component Type: .NET Class, 100% Managed Code

Compatible Containers: Microsoft SQL Server 2008, Microsoft SQL Server 2005

Keywords: SQLDistributions

totally sql

Math Stats Mathematics Mathematical Statistic Statistical

SQL query language

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