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

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in Maths and Stats

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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)

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