lognormal#

Generates lognormally distributed random numbers.

Description#

The lognormal class object is used in the generate function to provide random numbers with average of distribution (m, a) and standard deviation (s, \(\sigma\)) of subject normal distribution, displacement (displ, b), and scalefactor (scale, \(\beta\)), where \(a, \sigma, b, \beta \in \mathbb{R}; \sigma > 0, \beta > 0\).

The probability density function is given by:

\[\begin{split}f_{a, \sigma, b, \beta} (x) = \begin{cases} \frac{1}{\sigma (x - b) \sqrt {2\pi}} \exp \left( -\frac{\ln( \frac{x - b}{\beta}) - a)^2}{2\sigma^2} \right), & x > b \\ 0, & x \leq b \end{cases}\end{split}\]

The cumulative distribution function is as follows:

\[\begin{split}F_{a, \sigma, b, \beta} (x) = \begin{cases} \Phi \left(\frac{\ln( \frac{x - b}{\beta}) - a}{\sigma}\right), & x > b \\ 0, & x \leq b \end{cases}\end{split}\]

API#

Syntax#

template<typename RealType, typename Method>
class lognormal {
public:
   using method_type = Method;
   using result_type = RealType;

   lognormal() : lognormal((RealType)0.0, (RealType)1.0, (RealType) 0.0, (RealType)1.0){}
   explicit lognormal(RealType m, RealType s, RealType displ = (RealType)0.0, RealType scale = (RealType)1.0);
   explicit lognormal(const param_type& pt);

   RealType m() const;
   RealType s() const;
   RealType displ() const;
   RealType scale() const;
   param_type param() const;
   void param(const param_type& pt);
};

Include Files#

  • oneapi/mkl/rng/device.hpp

Template Parameters#

typename Type

Type of the produced values. The specific values are as follows:

  • float

  • double

typename Method

Generation method. The specific values are as follows:

  • oneapi::mkl::rng::device::lognormal_method::by_default

  • oneapi::mkl::rng::device::lognormal_method::box_muller2

See brief descriptions of the methods in Distributions Template Parameter Method.

Note: To enable oneapi::mkl::rng::device::lognormal_method::box_muller2 based on Vector Math functions, define the MKL_RNG_USE_BINARY_CODE macro and link static oneMKL libraries according to the output produced by Intel® oneAPI Math Kernel Library Link Line Advisor. It may improve performance on some hardware.

Input Parameters#

Name

Type

Description

m

RealType (float, double)

Average a of the subject normal distribution.

s

RealType (float, double)

Standard deviation \(\sigma\) of the subject normal distribution.

displ

RealType (float, double)

Displacement displ.

scale

RealType (float, double)

Scalefactor scale.