How to declare Rayleigh random variables ?

Hello all, how to declare Rayleigh random variables in the following case:

Suppose we have two vectors, "sr" vector is of source and "ta" vector is of target as shown below.

My query is that how we can have Rayleigh random variable between each elements of two vectors.

Any help in this regard will be highly appreciated.

sr = [1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4]; % various possible sources
ta = [2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5]; % various possible targets 

Answer 1

[Image Analyst]

Did you try random in the Statistics and Machine Learning Toolbox. It can produce random numbers drawn from a Rayleigh distribution.

help random

 RANDOM Generate random arrays from a specified distribution.
    R = RANDOM(NAME,A) returns an array of random numbers chosen from the
    one-parameter probability distribution specified by NAME with parameter
    values A.
 
    R = RANDOM(NAME,A,B) or R = RANDOM(NAME,A,B,C) returns an array of random
    numbers chosen from a two- or three-parameter probability distribution
    with parameter values A, B (and C).
 
    The size of R is the common size of the input arguments.  A scalar input
    functions as a constant matrix of the same size as the other inputs.
 
    R = RANDOM(NAME,A,M,N,...) or R = RANDOM(NAME,A,[M,N,...]) returns an
    M-by-N-by-... array of random numbers for a one-parameter distribution.
    Similarly, R = RANDOM(NAME,A,B,M,N,...) or R = RANDOM(NAME,A,B,[M,N,...]),
    and R = RANDOM(NAME,A,B,C,M,N,...) or R = RANDOM(NAME,A,B,C,[M,N,...]),
    return an M-by-N-by-... array of random numbers for a two- or
    three-parameter distribution.
 
 
    NAME can be:
 
       'beta'  or 'Beta',
       'bino'  or 'Binomial',
       'burr'  or 'Burr',
       'chi2'  or 'Chisquare',
       'exp'   or 'Exponential',
       'ev'    or 'Extreme Value',
       'f'     or 'F',
       'gam'   or 'Gamma',
       'gev'   or 'Generalized Extreme Value',
       'gp'    or 'Generalized Pareto',
       'geo'   or 'Geometric',
       'hn'    or 'Half Normal',
       'hyge'  or 'Hypergeometric',
       'logn'  or 'Lognormal',
       'nbin'  or 'Negative Binomial',
       'ncf'   or 'Noncentral F',
       'nct'   or 'Noncentral t',
       'ncx2'  or 'Noncentral Chi-square',
       'norm'  or 'Normal',
       'poiss' or 'Poisson',
       'rayl'  or 'Rayleigh',
       'stable'or 'Stable',
       't'     or 'T',
       'unif'  or 'Uniform',
       'unid'  or 'Discrete Uniform',
       'wbl'   or 'Weibull'.
 
    Partial matches are allowed and case is ignored.
 
    RANDOM is a generic function that accepts a distribution by name. It is
    faster to use a more specialized function when possible, such as RANDN
    or NORMRND for the normal distribution.
 
    See also CDF, ICDF, MLE, PDF.

    Documentation for random
       doc stats/prob.NormalDistribution/random

    Other uses of random

       classreg.regr.CompactGeneralizedLinearModel/random
       classreg.regr.CompactLinearModel/random
       GeneralizedLinearMixedModel/random
       gmdistribution/random
       LeastSquaresResults/random
       LinearMixedModel/random
       MultinomialRegression/random
       NLMEResults/random
       NonLinearModel/random
       piecewisedistribution/random
       prob.NormalDistribution/random
       prob.ProbabilityDistribution/random
       prob.UnivariateDistribution/random
       RepeatedMeasuresModel/random

Otherwise see my attached demo.