用matlab怎么做bootstrap方法和随机抽样

设数据存放于向量a中，需要重复n次简单随机采样，程序及说明如下：

m=length(a)%dimension

idx= ceil(m*rand(1,n)) %generate n random index between 1 and m

b = a(idx) % sampling

这个是有放回的抽样，即两次有可能抽到同一个元素，用于Bootstrap方法中

简单随机抽样原则上应是有放回的抽样，使用randsample(X,N,1)但大多数时候，人们常采用无放回的抽样，对应于randsample(X,N,0)，对于N<0.05lenght(X)的情况与有放回抽样的结果相比无太大差别

function f=Gamma_bootstrap(k,gamma,lambda,tao,N,n,B,arfa)

X= gamrnd(k,lambda,1,N)

Y= gamrnd(gamma,tao,1,N)

X_bar=mean(X)

Y_bar=mean(Y)

lambda_bar=k/X_bar

tao_bar=gamma/Y_bar

rou_hat=tao_bar/lambda_bar

R_hat=1-fcdf(gamma/k/rou_hat,2*k,2*gamma)

for i=1:B

XX= gamrnd(k,lambda_bar,1,n)

YY= gamrnd(gamma,tao_bar,1,n)

X_star=mean(XX)

Y_star=mean(YY)

lambda_star(i)=k/X_star

tao_star(i)=gamma/Y_star

rou_star(i)=tao_star(i)./lambda_star(i)

R_star(i)=1-fcdf(gamma/k./rou_star(i),2*k,2*gamma)

end

% Lambda=var(lambda_star)

% MSE_Lambda=var(lambda_star)*(n-1)/n+(mean(lambda_star)-lambda)^2

% Tao=var(tao_star)

% MSE_Tao=var(tao_star)*(n-1)/n+(mean(tao_star)-tao)^2

rou=tao/lambda

real_R=1-fcdf(gamma/k./rou,2*k,2*gamma)

R_star_mean=mean(R_star)

R_star_variance=var(R_star)

R_star_sort=sort(R_star)

R_quantile_left=R_star_sort(round((B+1)*(1-arfa/2)))

R_quantile_right=R_star_sort(round((B+1)*arfa/2))

left_R=2*R_hat-R_quantile_left

right_R=2*R_hat-R_quantile_right

length=right_R-left_R

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