여러 확률분포들의 단일 변수 PDF 및 CDF 관련 MATLAB code

1. Normal Distribution

관련 MATLAB 함수: normpdf, normcdf, norminv, normrnd

 

--- MATLAB code ---

% normal distribution
mu = 10;
sigma = 2;
x = 0:0.1:mu*2;
y = normpdf(x,mu,sigma);     % normal pdf 값
plot(x, y)
y = normcdf(x, mu, sigma);    % normal cdf 값
plot(x, y)
y = norminv(0.5, mu, sigma)  % normcdf의 역함수
normrnd(mu, sigma, 2)         % normpdf에 맞게 난수 생성

 

normal distribution PDF & CDF

 

2. Lognormal Distribution

관련 MATLAB 함수: lognpdf, logncdf, logninv, lognrnd

 

--- MATLAB code ---

% lognormal distribution
mu = 3;
sigma = 1;
x = 0:0.1:mu*10;
y = lognpdf(x,mu,sigma);     % lognormal pdf 값
plot(x, y)
y = logncdf(x, mu, sigma);   % lognormal cdf 값
plot(x, y)
y = logninv(0.5, mu, sigma)  % lognormcdf의 역함수
lognrnd(mu, sigma, 2)        % lognormpdf에 맞게 난수 생성

 

lognormal distribution PDF & CDF

 

3. Chi-Square Distribution

관련 MATLAB 함수: chi2pdf, chi2cdf, chi2inv, chi2rnd

 

--- MATLAB code ---

% Chi-Square distribution
nu = 10;
x = 0:0.1:nu*2;
y = chi2pdf(x,nu);        % Chi-Square distribution pdf 값
plot(x, y)
y = chi2cdf(x, nu);       % Chi-Square distribution cdf 값
plot(x, y)
y = chi2inv(0.5, nu)      % Chi-Square distribution cdf의 역함수
chi2rnd(nu, 2)            % Chi-Square distribution pdf에 맞게 난수 생성

 

Chi-square distribution PDF & CDF

 

4. t-Distribution

관련 MATLAB 함수: tpdf, tcdf, tinv, trnd

 

--- MATLAB code ---

% t-distribution
nu = 5;
x = -nu*2:0.1:nu*2;
y = tpdf(x,nu);        % t-distribution pdf 값
plot(x, y)
y = tcdf(x, nu);       % t-distribution cdf 값
plot(x, y)
y = tinv(0.7, nu)      % t-distribution cdf의 역함수
trnd(nu, 2)            % t-distribution pdf에 맞게 난수 생성

 

t distribution PDF & CDF

 

5. F-Distribution

관련 MATLAB 함수: fpdf, fcdf, finv, frnd

 

--- MATLAB code ---

% F-distribution
nu1 = 5;
nu2 = 25;
x = 0:0.1:nu1*2;
y = fpdf(x, nu1, nu2);   % F-distribution pdf 값
plot(x, y)
y = fcdf(x, nu1, nu2);   % F-distribution cdf 값
plot(x, y)
y = finv(0.5, nu1, nu2)  % F-distribution cdf의 역함수
frnd(nu1, nu2, 2)        % F-distribution pdf에 맞게 난수 생성

 

F distribution PDF & CDF

 

6. Uniform Distribution

관련 MATLAB 함수: unifpdf, unifcdf, unifinv, unifrnd

 

--- MATLAB code ---

% uniform distribution
a = 5;
b = 10;
x = 0:0.1:15;
y = unifpdf(x, a, b);   % uniform distribution pdf 값
plot(x, y)
y = unifcdf(x, a, b);   % uniform distribution cdf 값
plot(x, y)
y = unifinv(0.5, a, b)  % uniform distribution cdf의 역함수
unifrnd(a, b, 2)        % uniform distribution pdf에 맞게 난수 생성

 

uniform distribution PDF & CDF

 

7. Exponential Distribution

관련 MATLAB 함수: exppdf, expcdf, expinv, exprnd

 

--- MATLAB code ---

% exponential distribution
lambda = 1;
x = 0:0.1:10;
y = exppdf(x, lambda);   % exponential distribution pdf 값
plot(x, y)
y = expcdf(x, lambda);   % exponential distribution cdf 값
plot(x, y)
y = expinv(0.5, lambda)  % exponential distribution cdf의 역함수
exprnd(lambda, 2)        % exponential distribution pdf에 맞게 난수 생성

 

exponential distribution PDF & CDF

 

8. Gamma Distribution

관련 MATLAB 함수: gampdf, gamcdf, gaminv, gamrnd

 

--- MATLAB code ---

% gamma distribution
lambda = 2;
k = 3;
x = 0:0.1:10;
y = gampdf(x, k, 1/lambda);   % gamma distribution pdf 값
plot(x, y)
y = gamcdf(x, k, 1/lambda);   % gamma distribution cdf 값
plot(x, y)
y = gaminv(0.5, k, 1/lambda)  % gamma distribution cdf의 역함수
gamrnd(k, 1/lambda, 2)        % gamma distribution pdf에 맞게 난수 생성

 

gamma distribution PDF & CDF

 

9. Weibull Distribution

관련 MATLAB 함수: wblpdf, wblcdf, wblinv, wblrnd

 

--- MATLAB code ---

% Weibull distribution
scale = 1; % scale parameter
shape = 2; % shape parameter
x = 0:0.001:3;
y = wblpdf(x, scale, shape);   % Weibull distribution pdf 값
plot(x, y)
y = wblcdf(x, scale, shape);   % Weibull distribution cdf 값
plot(x, y)
y = wblinv(0.5, scale, shape)  % Weibull distribution cdf의 역함수
wblrnd(scale, shape, 2)        % Weibull distribution pdf에 맞게 난수 생성

 

Weibull distribution PDF & CDF