# Description of Distribution Generator Tests

This section describes the available Distribution Generator Tests:

# Distribution Moments Test

#### Test Purpose

The test verifies that sample moments of a given distribution agree with theoretical moments. Sample mean (first order moment) and sample variance (central moment of the second order) are considered as stable responses.

# Chi-Squared Goodness-of-Fit Test

#### Test Purpose

The test verifies that the sample distribution function agrees with the hypothesized distribution. A chi-squared V statistic with the number of degrees of freedom that is minus one from the number of the intervals of partition is considered a stable response.

# Performance

The following factors influence the performance of an RNG of a given distribution:

1. architecture and configuration of the hardware and software

2. performance of the underlying BRNG

3. method of transformation

4. number of random numbers to be generated (size of the output vector)

5. parameters of a given probability distribution

# Continuous Distribution Functions

This section describes VSL Continuous Distribution Functions:

# Uniform (VSL_RNG_METHOD_UNIFORM_STD/ VSL_RNG_METHOD_UNIFORM_STD_ACCURATE)

Random number generator of uniform distribution over the real interval [a,b). You may identify the underlying BRNG by passing the random stream descriptor stream as a parameter. Then the Uniform function calls real implementation (of single precision for vsRngUniform and of double precision for vdRngUniform) of this BRNG.

# Gaussian (VSL_RNG_METHOD_GAUSSIAN_BOXMULLER)

Random number generator of normal (Gaussian) distribution with parameters a and s. You can obtain any successive random number x of the standard normal distribution according to the formula

,

# Gaussian (VSL_RNG_METHOD_GAUSSIAN_BOXMULLER2)

Random number generator of normal (Gaussian) distribution with parameters a and s. You can produce a successive pair of the random numbers x1, x2 of the standard normal distribution according to the formula

# Gaussian (VSL_RNG_METHOD_GAUSSIAN_ICDF)

Random number generator of normal (Gaussian) distribution with parameters a and s. You can obtain any successive random number x of the standard normal distribution by the inverse transformation method from the following formula: