?? randraw.m
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% 1. y = randraw('anglit', [], [1 1e5]); % 2. y = randraw('anglit', [], 1, 1e5); % 3. y = randraw('anglit', [], 1e5 ); % 4. y = randraw('anglit', [10 3], [1e5 1] ); % 5. randraw('anglit'); % % END anglit HELP checkParamsNum(funcName, 'Anglit', 'anglit', distribParams, [0, 2]); if numel(distribParams)==2 t = distribParams(1); s = distribParams(2); validateParam(funcName, 'Anglit', 'anglit', '[t, s]', 's', s, {'> 0'}); else t = 0; s = pi/4; end out = t + s * (4/pi*asin(sqrt(rand(sampleSize)))-1); case {'arcsin'} % START arcsin HELP % THE ARC-SINE DISTRIBUTION % % pdf(y) = 1 ./ (pi*sqrt(y.*(1-y))); 0<y<1; % cdf(y) = 2*asin(sqrt(y))/pi; 0<y<1; % % Mean = 0.5; % Variance = 0.125; % % PARAMETERS: % None % % SUPPORT: % y, 0<y<1 % % CLASS: % Continuous symmetric distributions % NOTES: % The arc-sine distribution is a special case of the beta distribution % with both parameters equal to 1/2. The generalized arc-sine distribution % is the special case of the beta distribution where the two parameters sum % to 1 but are not necessarily equal to 1/2. % % USAGE: % randraw('arcsin', [], sampleSize) - generate sampleSize number % of variates from the Arc-sine distribution; % randraw('arcsin') - help for the Arc-sine distribution; % % EXAMPLES: % 1. y = randraw('arcsin', [], [1 1e5]); % 2. y = randraw('arcsin', [], 1, 1e5); % 3. y = randraw('arcsin', [], 1e5 ); % 4. randraw('arcsin'); % SEE ALSO: % U distribution % END arcsin HELP checkParamsNum(funcName, 'Arcsin', 'arcsin', distribParams, 0); out = sin( rand(sampleSize)*pi/2 ).^2; case {'bernoulli', 'bern'} % START bernoulli HELP START bern HELP % THE BERNOULLI DISTRIBUTION % % pdf(y) = p.^y .* (1-p).^(1-y); % cdf(y) = (y==0)*(1-p) + (y==1)*1; % % PARAMETERS: % p is a probability of success; (0<p<1) % % SUPPORT: % y = [0 1]; % % CLASS: % Discrete distributions % % USAGE: % randraw('bern', p, sampleSize) - generate sampleSize number % of variates from the Bernoulli distribution with probability of success p % randraw('bern') - help for the Bernoulli distribution; % % EXAMPLES: % 1. y = randraw('bern', 0.5, [1 1e5]); % 2. y = randraw('bern', 0.1, 1, 1e5); % 3. y = randraw('bern', 0.9, 1e5 ); % 4. randraw('bern'); % END bernoulli HELP END bern HELP checkParamsNum(funcName, 'Bernoulli', 'bernoulli', distribParams, 1); validateParam(funcName, 'Bernoulli', 'bernoulli', 'p', 'p', distribParams(1), {'>=0','<=1'}); out = double( rand( sampleSize ) < distribParams ); case {'beta', 'powerfunction', 'powerfunc'} % START beta HELP % THE BETA DISTRIBUTION % % ( sometimes: Power Function distribution ) % % Standard form of the Beta distribution: % pdf(y) = y.^(a-1).*(1-y).^(b-1) / beta(a, b); % cdf(y) = betainc(y,a,b), if (y>=0 & y<=1); 0, if x<0; 1, if x>1 % % Mean = a/(a+b); % Variance = (a*b)/((a+b)^2*(a+b+1)); % % General form of the Beta distribution: % pdf(y) = (y-m).^(a-1).*(n-y).^(b-1) / (beta(a, b)*(n-m)^(a+b-1)); % cdf(y) = betainc((y-m)/(n-m),a,b), if (y>=m & y<=n); 0, if x<m; 1, if x>n % % Mean = (n*a + m*b)/(a+b); % Variance = (a*b)*(n-m)^2/((a+b)^2*(a+b+1)); % % PARAMETERS: % a>0 - shape parameter % b>0 - shape parameter % m - location % n -scale (upper bound); n>=m % % SUPPORT: % y, 0<=y<=1 - standard beta distribution % or % y, m<=y<=n - generalized beta distribution % % CLASS: % Continuous skewed distributions % % USAGE: % randraw('beta', [a, b], sampleSize) - generate sampleSize number % of variates from standard beta distribution with shape parameters % 'a' and 'b' % randraw('beta', [m, n, a, b], sampleSize) - generate sampleSize number % of variates from generalized beta distribution on the interval [m, n] % with shape parameters 'a' and 'b'; % randraw('beta') - help for the Beta distribution; % EXAMPLES: % 1. y = randraw('beta', [0.2 0.9], [1 1e5]); % 2. y = randraw('beta', [0.6 3.2], 1, 1e5); % 3. y = randraw('beta', [-10 20 3.1 6.2], 1e5 ); % 4. y = randraw('beta', [3 4 5.3 0.7], [1e5 1] ); % 5. randraw('beta'); % END beta HELP % Refernce: % Dagpunar, John. % Principles of Random Variate Generation. % Oxford University Press, 1988. % % max_ab < 0.5 Joehnk's algorithm % 1 < min_ab Cheng's algortihm BB % min_ab <= 1 <= max_ab Atkinson's switching algorithm % 0.5<= max_ab < 1 Atkinson's switching algorithm checkParamsNum(funcName, 'Beta', 'beta', distribParams, [2, 4]); if numel(distribParams) == 2 a = distribParams(1); b = distribParams(2); m = 0; n = 1; validateParam(funcName, 'Beta', 'beta', '[a, b]', 'a', a, {'> 0'}); validateParam(funcName, 'Beta', 'beta', '[a, b]', 'b', b, {'> 0'}); else m = distribParams(1); n = distribParams(2); a = distribParams(3); b = distribParams(4); validateParam(funcName, 'Beta', 'beta', '[m, n, a, b]', 'n-m', n-m, {'>= 0'}); validateParam(funcName, 'Beta', 'beta', '[m, n, a, b]', 'a', a, {'> 0'}); validateParam(funcName, 'Beta', 'beta', '[m, n, a, b]', 'b', b, {'> 0'}); end sampleSizeIn = sampleSize; sampleSize = [ 1, prod( sampleSizeIn ) ]; max_ab = max( a, b ); min_ab = min( a, b ); if max_ab < 0.5 % Use log(u1^a) and log(u2^b), rather than a and b, to avoid % underflow for very small a or b. loga = log(rand( sampleSize ))/a; logb = log(rand( sampleSize ))/b; logsum = (loga>logb).*(loga + log(1+ exp(logb-loga))) + ... (loga<=logb).*(logb + log(1+ exp(loga-logb))); out = exp(loga - logsum); indxs = find( logsum > 0); while ~isempty( indxs ) indxsSize = size( indxs ); loga = log(rand( indxsSize ))/a; logb = log(rand( indxsSize ))/b; logsum = (loga>logb).*(loga + log(1+ exp(logb-loga))) + ... (loga<=logb).*(logb + log(1+ exp(loga-logb))); l = (logsum <= 0); out( indxs( l ) ) = exp(loga(l) - logsum(l)); indxs = indxs( ~l ); end % Algorithm BB sum_ab = a + b; lambda = sqrt((sum_ab-2)/(2*a*b-sum_ab)); c = min_ab+1/lambda; u1 = rand( sampleSize ); u2 = rand( sampleSize ); v = lambda*log(u1./(1-u1)); z = u1.*u1.*u2; clear('u1'); clear('u2'); w = min_ab*exp(v); r = c*v-1.38629436112; clear('v'); s = min_ab+r-w; if a == min_ab out = w./(max_ab+w); else out = max_ab./(max_ab+w); end t = log(z); indxs = find( (s+2.609438 < 5*z) & (r+sum_ab*log(sum_ab./(max_ab+w)) < t) ); clear('v'); clear('z'); clear('w'); clear('r'); while ~isempty( indxs ) indxsSize = size( indxs ); u1 = rand( indxsSize ); u2 = rand( indxsSize ); v = lambda*log(u1./(1-u1)); z = u1.*u1.*u2; clear('u1'); clear('u2'); w = min_ab*exp(v); r = c*v-1.38629436112; clear('v'); s = min_ab+r-w; t = log(z); l = (s+2.609438 >= 5*z) | (r+sum_ab*log(sum_ab./(max_ab+w)) >= t); if a == min_ab out( indxs( l ) ) = w(l)./(max_ab+w(l)); else out( indxs( l ) ) = max_ab./(max_ab+w(l)); end indxs = indxs( ~l ); end elseif min_ab < 1 & max_ab > 1 % Atkinson's switching method t = (1-min_ab)/(1+max_ab - min_ab); r = max_ab*t/(max_ab*t + min_ab*(1-t)^max_ab); u1 = rand( sampleSize ); w = zeros( sampleSize ); l = u1 < r; w( l ) = t*(u1( l )/r).^(1/min_ab); l = ~l; w( l ) = 1- (1-t)*((1-u1(l))/(1-r)).^(1/max_ab); if a == min_ab out = w; else out = 1 - w; end u2 = rand( sampleSize ); indxs1 = find(u1 < r); indxs2 = find(u1 >= r); clear('u1'); indxs = [ indxs1( log(u2(indxs1)) >= (max_ab-1)*log(1-w(indxs1)) ), ... indxs2( log(u2(indxs2)) >= (min_ab-1)*log(w(indxs2)/t) ) ]; clear('u1'); clear('u2'); while ~isempty( indxs ) indxsSize = size( indxs ); u1 = rand( indxsSize ); w = zeros( indxsSize ); l = u1 < r; w( l ) = t*(u1( l )/r).^(1/min_ab); l = ~l; w( l ) = 1- (1-t)*((1-u1(l))/(1-r)).^(1/max_ab); u2 = rand( indxsSize ); indxs1 = find(u1 < r); indxs2 = find(u1 >= r); clear('u1'); l = logical( zeros( indxsSize ) ); l( [ indxs1( log(u2(indxs1)) < (max_ab-1)*log(1-w(indxs1)) ), ...?? 快捷鍵說明
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