Lognormal

Generates lognormally distributed random numbers.

Syntax

Fortran:

status = vsrnglognormal( method, stream, n, r, a, sigma, b, beta )

status = vdrnglognormal( method, stream, n, r, a, sigma, b, beta )

status = vsRngLognormal( method, stream, n, r, a, sigma, b, beta );

status = vdRngLognormal( method, stream, n, r, a, sigma, b, beta );

Include Files

The FORTRAN 77 interfaces are specified in the mkl_vsl.f77 include file, the Fortran 90 interfaces are specified in the mkl_vsl.f90 include file, and the C interfaces are specified in the mkl_vsl_functions.h include file.

Input Parameters

Name	Type	Description
method	FORTRAN 77: INTEGER Fortran 90: INTEGER, INTENT(IN) C: const int	Generation method. The specific values are as follows: `VSL_RNG_METHOD_LOGNORMAL_BOXMULLER2` `VSL_RNG_METHOD_LOGNORMAL_BOXMULLER2_ACCURATE` Inverse cumulative distribution function method
stream	FORTRAN 77: INTEGER4 stream(2) Fortran 90:* TYPE (VSL_STREAM_STATE), INTENT(IN) C: VSLStreamStatePtr	Fortran: Descriptor of the stream state structure. C: Pointer to the stream state structure
n	FORTRAN 77: INTEGER Fortran 90: INTEGER, INTENT(IN) C: const int	Number of random values to be generated
a	FORTRAN 77: REAL for vsrnglognormal DOUBLE PRECISION for vdrnglognormal Fortran 90: REAL, INTENT(IN) for vsrnglognormal DOUBLE PRECISION, INTENT(IN) for vdrnglognormal C: const float for vsRngLognormal const double for vdRngLognormal	Average `a` of the subject normal distribution
sigma	FORTRAN 77: REAL for vsrnglognormal DOUBLE PRECISION for vdrnglognormal Fortran 90: REAL, INTENT(IN) for vsrnglognormal DOUBLE PRECISION, INTENT(IN) for vdrnglognormal C: const float for vsRngLognormal const double for vdRngLognormal	Standard deviation σ of the subject normal distribution
b	FORTRAN 77: REAL for vsrnglognormal DOUBLE PRECISION for vdrnglognormal Fortran 90: REAL, INTENT(IN) for vsrnglognormal DOUBLE PRECISION, INTENT(IN) for vdrnglognormal C: const float for vsRngLognormal const double for vdRngLognormal	Displacement `b`
beta	FORTRAN 77: REAL for vsrnglognormal DOUBLE PRECISION for vdrnglognormal Fortran 90: REAL, INTENT(IN) for vsrnglognormal DOUBLE PRECISION, INTENT(IN) for vdrnglognormal C: const float for vsRngLognormal const double for vdRngLognormal	Scalefactor β.

Output Parameters

Name	Type	Description
r	FORTRAN 77: REAL for vsrnglognormal DOUBLE PRECISION for vdrnglognormal Fortran 90: REAL, INTENT(OUT) for vsrnglognormal DOUBLE PRECISION, INTENT(OUT) for vdrnglognormal C: float* for vsRngLognormal double* for vdRngLognormal	Vector of `n` lognormally distributed random numbers

Name

Type

Description

FORTRAN 77: REAL for vsrnglognormal

DOUBLE PRECISION for vdrnglognormal

Fortran 90: REAL, INTENT(OUT) for vsrnglognormal

DOUBLE PRECISION, INTENT(OUT) for vdrnglognormal

C: float* for vsRngLognormal

double* for vdRngLognormal

Vector of n lognormally distributed random numbers

Description

The Lognormal function generates lognormally distributed random numbers with average of distribution a and standard deviation σ of subject normal distribution, displacement b, and scalefactor β, where a, σ, b, β∈R ; σ > 0 , β > 0.

The probability density function is given by:

The cumulative distribution function is as follows:

Return Values

VSL_ERROR_OK, VSL_STATUS_OK: Indicates no error, execution is successful.
VSL_ERROR_NULL_PTR: stream is a NULL pointer.
VSL_RNG_ERROR_BAD_STREAM: stream is not a valid random stream.
VSL_RNG_ERROR_BAD_UPDATE: Callback function for an abstract BRNG returns an invalid number of updated entries in a buffer, that is, < 0 or > nmax.
VSL_RNG_ERROR_NO_NUMBERS: Callback function for an abstract BRNG returns 0 as the number of updated entries in a buffer.
VSL_RNG_ERROR_QRNG_PERIOD_ELAPSED: Period of the generator has been exceeded.