SQLDistributions

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)