function varargout = randraw(distribName, distribParams, varargin)%%   EFFICIENT RANDOM VARIATES GENERATOR%% See alphabetical list of the supported distributions below (over 50 distributions)%% 1)  randraw%           presents general help.% 2)  randraw( distribName )%           presents help for the specific distribution defined%           by usage string distribName (see table below).% 3)  Y = randraw( distribName, distribParams, sampleSize );%           returns array Y of size = sampleSize of random variates from distribName%           distribution with parameters distribParams%%               ALPHABETICAL LIST OF THE SUPPORTED DISTRIBUTIONS:%  ____________________________________________________________________% |      DISTRIBUTION NAME                    |   USAGE STRING         |% |___________________________________________|________________________|% |        Alpha                              |    'alpha'             |% |        Anglit                             |    'anglit'            |% |        Antilognormal                      |    'lognorm'           |% |        Arcsin                             |    'arcsin'            |% |        Bernoulli                          |    'bern'              |% |        Bessel                             |    'bessel'            |% |        Beta                               |    'beta'              |% |        Binomial                           |    'binom'             |% |        Bradford                           |    'bradford'          |% |        Burr                               |    'burr'              |% |        Cauchy                             |    'cauchy'            |% |        Chi                                |    'chi'               |% |        Chi-Square (Non-Central)           |    'chisqnc'           |% |        Chi-Square (Central)               |    'chisq'             |% |        Cobb-Douglas                       |    'lognorm'           |% |        Cosine                             |    'cosine'            |% |        Double-Exponential                 |    'laplace'           |% |        Erlang                             |    'erlang'            |% |        Exponential                        |    'exp'               |% |        Extreme-Value                      |    'extrval'           |% |        F (Central)                        |    'f'                 |% |        F (Non-Central)                    |    'fnc'               |% |        Fisher-Tippett                     |    'extrval'           |% |        Fisk                               |    'fisk'              |% |        Frechet                            |    'frechet'           |% |        Furry                              |    'furry'             |% |        Gamma                              |    'gamma'             |% |        Generalized Inverse Gaussian       |    'gig'               |% |        Generalized Hyperbolic             |    'gh'                |% |        Geometric                          |    'geom'              |% |        Gompertz                           |    'gompertz'          |% |        Gumbel                             |    'gumbel'            |% |        Half-Cosine                        |    'hcos'              |% |        Hyperbolic Secant                  |    'hsec'              |% |        Hypergeometric                     |    'hypergeom'         |% |        Inverse Gaussian                   |    'ig'                |% |        Laplace                            |    'laplace'           |% |        Logistic                           |    'logistic'          |% |        Lognormal                          |    'lognorm'           |% |        Lomax                              |    'lomax'             |% |        Lorentz                            |    'lorentz'           |% |        Maxwell                            |    'maxwell'           |% |        Nakagami                           |    'nakagami'          |% |        Negative Binomial                  |    'negbinom'          |% |        Normal                             |    'norm'              |% |        Normal-Inverse-Gaussian (NIG)      |    'nig'               |% |        Pareto                             |    'pareto'            |% |        Pareto2                            |    'pareto2'           |% |        Pascal                             |    'pascal'            |% |        Planck                             |    'planck'            |% |        Poisson                            |    'po'                |% |        Quadratic                          |    'quadr'             |% |        Rademacher                         |    'rademacher'        |% |        Rayleigh                           |    'rayl'              |% |        Rice                               |    'rice'              |% |        Semicircle                         |    'semicirc'          |% |        Skellam                            |    'skellam'           |% |        Student's-t                        |    't'                 |% |        Triangular                         |    'tri'               |% |        Truncated Normal                   |    'normaltrunc'       |% |        Tukey-Lambda                       |    'tukeylambda'       |% |        U-shape                            |    'u'                 |% |        Uniform (continuous)               |    'uniform'           |% |        Von Mises                          |    'vonmises'          |% |        Wald                               |    'wald'              |% |        Weibull                            |    'weibull'           |% |        Wigner Semicircle                  |    'wigner'            |% |        Yule                               |    'yule'              |% |        Zeta                               |    'zeta'              |% |        Zipf                               |    'zipf'              |% |___________________________________________|________________________|%  Version 2.0 - August 2007%         1) New distributions support: Nakagami and Rician !%         2) Small typo corrections in comments%  Version 1.8 - February 2007%         GIG distribution (thanks to Mr. Demetris Lamnisos)%           Computational exceptions in the reparameterized GIG generation were fixed%  Version 1.7 - December 2006%         GIG distribution (thanks to Dr. Junbin Gao)%           Computational exceptions in the reparameterized GIG generation were fixed%  Version 1.6 - September 2006%         Exception handling: BINOMIAL distribution - special case for n*p~=0%         Geometric distibution: additional note in help section%  Version 1.5 - December 2005%        'true' and 'false' functions were replased by ones and zeros to support Matlab releases%         below 6.5%  Version 1.4 - September 2005 -%      Bugs fix:%        1) GAMMA distribution (thanks to Earl Lawrence):%             special case for a<1%        2) GIG distribution (thanks to Panagiotis Braimakis):%            typo in help%            code adjustment to overcome possible computational overflows%        3) CHI SQUARE distribution%            typo in help%  Version 1.3 - July 2005 -%      Bug fix:%         Typo in GIG distribution generation:%         should be 'out' instead of 'x' in lines 1852 and 1858%  Version 1.2 - May 2005  -%      Bugs fix:%        1) Poisson distribution did not work for lambda < 21.4. Typo ( ti instead of t )%        2) GIG distribution:  support to chi=0 or psi=0 cases%        3) Beta distribution: column sampleSize%        4) Cauchy distribution: typo in example%        5) Chi distribution:   typo in example%        6) Non-central F distribution:  number of input parameters%        7) INVERSE GAUSSIAN (IG) distribution: typo in example%%  Version 1.1 - April 2005 -  Bug fix:   Generation from binomial distribution using only 'binomial'%                                   usage string was changed to 'binom' ( 'binomial' works too ).%  Version 1.0 - March 2005 -  Initial version%  Alex Bar Guy  &  Alexander Podgaetsky%    alex@wavion.co.il% These programs are distributed in the hope that they will be useful,% but WITHOUT ANY WARRANTY; without even the implied warranty of% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.% Any comments and suggestions please send to:%    alex@wavion.co.il% Reference links:%   1) http://mathworld.wolfram.com/topics/StatisticalDistributions.html%   2) http://en.wikipedia.org/wiki/Category:Probability_distributions%   3) http://www.brighton-webs.co.uk/index.asp%   4) http://www.jstatsoft.org/v11/i03/v11i03.pdf%   5) http://www.quantlet.com/mdstat/scripts/csa/html/node236.htmlfuncName = mfilename;if nargin == 0     help(funcName);     return;elseif nargin == 1     runMode = 'distribHelp';elseif nargin == 2     runMode = 'genRun';     sampleSize = [1 1];else     runMode = 'genRun';     sampleSize = [varargin{1:end}];enddistribNameInner = lower( distribName( ~isspace( distribName ) ) );if strcmp(runMode, 'distribHelp')     fid = fopen( [ funcName '.m' ], 'r' );     printHelpFlag = 0;     while 1          tline = fgetl( fid );          if ~ischar( tline )               fprintf( '\n Unknown distribution name ''%s''.\n', distribName );               break;          end          if ~isempty( strfind( tline, [ 'END ', distribNameInner,' HELP' ] ) )               printHelpFlag = 0;               break;          end          if printHelpFlag               startPosition = strfind( tline, ' % ' ) + 3;               printLine = tline( startPosition : end );               if ~strcmp( funcName, 'randraw' )                    indxs = strfind( printLine, 'randraw' );                    while ~isempty( indxs )                         headLine = printLine( 1:indxs(1)-1 );                         tailLine = printLine( indxs(1)+7:end );                         printLine = [ headLine, funcName, tailLine ];                         indxs = strfind( printLine, 'randraw' );                    end               end               pause(0.02);               fprintf( '\n%s', printLine );          end          if ~isempty( strfind( tline, [ 'START ', distribNameInner,' HELP' ] ) )               printHelpFlag = 1;          end     end     fprintf( '\n\n' );     fclose( fid );     if nargout > 0          varargout{1} = [];     end     return;endif length(sampleSize) == 1     sampleSize = [ sampleSize, 1 ];endif strcmp(runMode, 'genRun')     runExample = 0;     plotFlag = 0;     dbclear if warning;     out = [];     if prod(sampleSize) > 0          switch lower( distribNameInner )               case {'alpha'}                    % START alpha HELP                    % THE ALPHA DISTRIBUTION                    %                    % pdf(y) = b*normpdf(a-b./y) ./ (y.^2*normcdf(a)); y>0; a>0; b>0;                    % cdf(y) = normcdf(a-b./y)/normcdf(a); y>0; a>0; b>0;                    %   where normpdf(x) = 1/sqrt(2*pi) * exp(-1/2*x.^2); is the standard normal PDF                    %         normcdf(x) = 0.5*(1+erf(y/sqrt(2))); is the standard normal CDF                    %                    % PARAMETERS:                    %   a - shape parameter (a>0)                    %   b - shape parameter (b>0)                    %                    % SUPPORT:                    %   y,  y>0                    %                    % CLASS:                    %   Continuous skewed distributions                    %                    % USAGE:                    %   randraw('alpha', [], sampleSize) - generate sampleSize number                    %         of variates from Alpha distribution with shape parameters a and b;                    %   randraw('alpha') - help for Alpha distribution;                    %                    % EXAMPLES:                    %  1.   y = randraw('alpha', [1 2], [1 1e5]);                    %  2.   y = randraw('alpha', [2 3], 1, 1e5);                    %  3.   y = randraw('alpha', [10 50], 1e5 );                    %  4.   y = randraw('alpha', [20.5 30.5], [1e5 1] );                    %  5.   randraw('alpha');                    % END alpha HELP                    % References:                    % 1. doc erf                    checkParamsNum(funcName, 'Alpha', 'alpha', distribParams, [2]);                    a  = distribParams(1);                    b  = distribParams(2);                    validateParam(funcName, 'Alpha', 'alpha', '[a, b]', 'a', a, {'> 0'});                    validateParam(funcName, 'Alpha', 'alpha', '[a, b]', 'b', b, {'> 0'});                    out = b ./ ( a - norminv(normcdf(a)*rand(sampleSize)) );               case {'anglit'}                    % START anglit HELP                    % THE ANGLIT DISTRIBUTION                    %                    % Standard form of anglit distribution:                    %   pdf(y) = sin(2*y+pi/2);  -pi/4 <= y <= pi/4;                    %   cdf(y) = sin(y+pi/4).^2; -pi/4 <= y <= pi/4;                    %                    %   Mean = Median = Mode = 0;                    %   Variance = (pi/4)^2 - 0.5;                    %                    % General form of anglit distribution:                    %   pdf(y) = sin(pi/2*(y-t)/s+pi/2);  t-s <= y <= t+s; s>0                    %   cdf(y) = sin(pi/4*(y-t)/s+pi/4).^2;  t-s <= y <= t+s; s>0                    %                    %   Mean = Median = Mode = t;                    %   Variance = ???????;                    %                    % PARAMETERS:                    %   t - location                    %   s -scale; s>0                    %                    % SUPPORT:                    %   y,   -pi/4 <= y <= pi.4   - standard Anglit distribution                    %    or                    %   y,   t-s <= y <= t+s  - generalized Anglit distribution                    %                    % CLASS:                    %   Continuous distributions                    %                    % USAGE:                    %   randraw('anglit', [], sampleSize) - generate sampleSize number                    %         of variates from standard Anglit distribution;                    %   randraw('anglit', [t, s], sampleSize) - generate sampleSize number                    %         of variates from generalized Anglit distribution                    %         with location parameter 't' and scale parameter 's';                    %   randraw('anglit') - help for Anglit distribution;                    %                    % EXAMPLES: