随机模拟和统计主要结果分析命令

最大值(最小值)

max（min）

M = max(A)M = max([23 42 37 18 52])

M = max(A,[],dim,nanflag)A=[ -0.5 3.9 NaN 0.3]M = max(A,[],'includenan')

[M,I] = max(A,[],___,'linear');A = [1 2 3; 4 5 6][M,I] = max(A,[],2,'linear')

C = max(A,B,nanflag)A = rand(3,2);B = 0.5;C = max(A,B)

和(积)

sum（prod）

S = sum(A) S = sum(1:10)

S = sum(A,dim) S = sum(rand(3,4),2)

S = sum(A,vecdim) S= sum( rand(4,3,3),[1 2])

S = sum(A,vecdim,nanflag)

累计和（累计积）

cumsum（comprod）

B = cumprod(A)B = cumprod(1:5)

B = cumprod(A,dim) B = cumprod(randn(5,3),2)

B = cumprod(A,direction) A = randi([3,10],3)B = cumprod(A,'reverse')

B = cumprod(A,nanflag)

均值

mean

M = mean(A) M = mean(randi([3,10],3))

M = mean(A,dim)M = mean(randi([3,10],3),3)

M = mean(A,vecdim)

M = mean(___,nanflag)

标准差

std

S = std(A) S = std(randi([4,10],7))

S = std(A,w,dim)S = std(randi([4,10],7),0,2)

S = std(A,w,vecdim)

S = std(___,nanflag)

方差

var

V = var(A,w) ;A=randi([4,10],3)var(A,[0.5 0.2 0.3])

V = var(A,w,dim)A=randi([4,10],3)var(A,[0.5 0.2 0.3],2)

V = var(A,w,vecdim)

V = var(___,nanflag)

协方差

cov

C = cov(A)C = cov(randi([4,10],3)

C = cov(A,B)A = [3 6 4];B = [7 12 -9];cov(A,B)

C = cov(___,w)

C = cov(___,nanflag)

相关系数

corrcoef

R = corrcoef(A)A = [rand(6,1) rand(6,1)];

R = corrcoef(A,B) A = randn(10,1);B = randn(10,1);

[R,P,RL,RU] = corrcoef(___)

___ = corrcoef(___,Name,Value)

排序

sort

B = sort(A);A = [9 0 -7 -10 4 2]

B = sort(A,dim) B = sort(randi([4,10],3),2)

B = sort(___,direction);B = sort(randi([4,10],3),'descend')

[B,I] =sort(A,dim,Name,Value)

中值

median

M = median(A,'all') A=randi([4,10],3),

M = median(A,dim) M = median(randi([4,10],3),2)

M = median(A,vecdim)

M = median(A,vecdim,nanflag)

百分位数

prctile

Y = prctile(X,p)

Y = prctile(X,p,dim)

Y = prctile(X,p,vecdim)

Y = prctile(X,p,vecdim,'Method')

条形图

bar

bar(y)

bar(x,y)

bar(x,y,Name,Value)

b =bar(x,y,Name,Value)

频数图

histogram

histogram(X)

histogram(X,edges)

histogram(X,Name,Value)

h = histogram(X,Name,Value)

[0,1]均匀分布

rand

X = rand(n)

X = rand(x,y)

r = randi([10 50],1,5)

r = rand(1,4,'single')

随机排列

randperm

p = randperm(n) r = randperm(6)

p = randperm(n,k)r1 = randperm(8,4)

随机数

random

Y = random(gm)

Y = random(gm,n)

[Y,compIdx] = random(gm,n)

离散均匀随机

unidrnd

r = unidrnd(n)r=unidrnd(1:10:100)

r =unidrnd(n,sz1,.,szN)R_array=unidrn(100,2,3)

r = unidrnd(n,sz)R_array = unidrnd(100,[2,3])

均匀分布随机

unifrnd

r = unifrnd(a,b)r = unifrnd(0,1)

r =unifrnd(a,b,sz1,...,szN)r1 = unifrnd(0,1:5)

r = unifrnd(a,b,sz)r2 = unifrnd(0,1,[2 3])

正态分布随机

normrnd

r = normrnd(0,1)r = normrnd(0,1)

r =normrn(mu,sigma,sz1,.szN) r = normrnd(3,10,4,3)

r = normrn(a,b,sz)r =normrnd(3,10,[1,5])

二项分布随机

binornd

r = binornd(n,p) r=binornd(10:10:60,1./[10:10:60])

r =binornd(n,p,sz1,...,szN)r_array=binorn(100,0.2,2,3)

r = binornd(n,p,sz)binornd(100,0.2,[2 3])

泊松分布随机

poissrnd

r = poissrnd(lambda)r = poissrnd(10:2:20)

r = poissrnd(lambda,sz1,...,szN)r_array = poissrnd(20,3,4)

r = poissrnd(lambda,sz) r_array = poissrnd(30,[1 6])

多维正态随机数

mvnrnd

R = mvnrnd(mu,sigma)R = mvnrnd(rand(4,3),eye(3))

R = mvnrnd(mu,sigma,n)R = mvnrnd( [2 3],[1 1.5; 1.5 3],100)

概率函数

pdf

y = pdf(gm,X)

pdf(gmdistribution([1 2;-3 -5],[1 1]),[0 0;1 2;3 3;5 3])

正态分布密度

normpdf

y = normpdf(x) y = normpdf([-2,-1,0,1,2])

y = normpdf(x,mu)y = normpdf([-2,-1,0,1,2],3)

y = normpdf(x,mu,sigma)y = normpdf([-2,-1,0,1,2],2,1)

累计概率函数

cdf

y = cdf('name',x,A)

y = cdf('name',x,A,B)

y = cdf(pd,x) p = cdf(makedist('Normal'),[-3:0.1:3])

正态分布函数

normcdf

p = normcdf(x) p = normcdf([-1:0.1:1])

p = normcdf(x,mu,sigma)p = normcdf([-1:0.1:1],2,0.5)

[p,pLo,pUp] = normcdf(x,mu,sigma,pCov) ;phat = mle(normrnd(5,2,1000,1))[~,pCov] = normlike([phat(1),phat(2)],normrnd(5,2,1000,1));[p,pLo,pUp] = normcdf(0,muHat,sigmaHat,pCov)

逆分布函数

icdf

x = icdf('name',p,A)

x = icdf('name',p,A,B)x2 = icdf(pd,p,0,1)

x = icdf(pd,p)；x = icdf(makedist('Normal','mu',0,'sigma',1),[0.1:0.1:0.9])

正态分布下分位数

norminv

x = norminv(p)x = norminv([0.1:0.1:0.9])

x = norminv(p,mu,sigma)x = norminv([ 0.01:0.1:1],2,1)

[x,xLo,xUp] = norminv(p,mu,sigma,pCov,alpha)phat = mle(normrnd(5,2,[1000,1]));[~,pCov] = normlike([phat(1),phat(2)],normrnd(5,2,[1000,1]));[x,xLo,xUp] = norminv(0.5,muHat,sigmaHat,pCov,0.01)

T分布下分位数

tinv

x = tinv(p,nu)x = tinv(0.95,50)

percentile = tinv(0.99,1:6)

分布下分位数

finv

X = finv(P,V1,V2) x = finv(0.95,5,10)

参数估计

mle

phat = mle(data,'distribution',dist) load carbigphat = mle(MPG,'distribution','burr')

phat = mle(data,'pdf',pdf,'start',start)x = ncx2rnd(8,3,1000,1);[phat,pci] =mle(x,'pdf',@(x,v,d)ncx2pdf(x,v,d),'start',[1,1])

phat = mle(data,'pdf',pdf,'start',start,'cdf',cdf) load('readmissiontimes.mat');custpdf = @(data,lambda) lambda*exp(-lambda*data);custcdf = @(data,lambda) 1-exp(-lambda*data);phat=mle(ReadmissionTime,'pdf',custpdf,'cdf',custcdf,'start',0.05,'Censoring',Censored)

mle(data,'nloglf',nloglf,'start',start)load('readmissiontimes.mat');custnloglf = @(lambda,data,cens,freq) - length(data)*log(lambda)+nansum(lambda*data);phat=mle(ReadmissionTime,'nloglf',custnloglf,'start',0.05)

正态参数估计

normfit

[muHat,sigmaHat] = normfit(x)x= normrnd(0,1,[100,1]);[muHat,sigmaHat] = normfit(x);

[muHat,sigmaHat,muCI,sigmaCI] = normfit(x,alpha)x = normrnd(3,5,[1000,1]);[muHat,sigmaHat,muCI,sigmaCI] = normfit(x,0.01)

[___] = normfit(x,alpha,censoring,freq,options)

单总体T检验

ttest

h = ttest(x) load stockreturnsx = stocks(:,3);[h,p,ci,stats] = ttest(x)

h = ttest(x,y,Name,Value)

h = ttest(x,m)

h = ttest(x,m,Name,Value)

双总体T检验

ttest2

h = ttest2(x,y);load examgrades;x = grades(:,1);y = grades(:,2);[h,p,ci,stats] = ttest2(x,y)

h = ttest2(x,y,Name,Value) ;load examgradesx = grades(:,1);y = grades(:,2);[h,p] = ttest2(x,y,'Vartype','unequal')

双分布秩检验

ranksum

p = ranksum(x,y);x = unifrnd(0,1,10,1);y = unifrnd(0.25,1.25,15,1);p = ranksum(x,y)

[p,h,stats] = ranksum(x,y);load mileage[p,h,stats] = ranksum(mileage(:,1),mileage(:,2))