参考教材《概率论与数理统计》第四版， 高等教育出版社  盛骤等编  P132

根据书中定义求得的结果与根据MATLAB的quantile和prctile得到的结果有一些差别，原因是计算方法不同。我编写如下MATLAB程序进行对比，找找其中的差别吧？

维基百科： https://en.wikipedia.org/wiki/Quantile  提供了9个公式。

clear,clc

x = [122,126,133,140,145,145,149,150,157,...

   162,166,175,177,177,183,188,199,212];

xs = sort(x); p = [0.1,0.25,0.5,0.75 0.975];

% 分位数

n = length(x); np = floor(n*p); r = n*p-np;

id = (r ==0); xnp(id) = (xs(np(id))+xs(np(id)+1))/2;

idn = (r~=0); xnp(idn) = xs(np(idn)+1);

xnp

%%%  下面用了循环，和不用循环结果相同，只是更易理解

for i = 1:length(p)

   if n*p(i)==np(i)

       xnp(i) = (xs(np(i))+xs(np(i)+1))/2;

   else

        xnp(i) = xs(np(i)+1);

   end

end

xnp

%plot

%%% MATLAB自带的命令，有细微差别, 感觉自带的比较合理

r = p*n;

k = floor(r+0.5); % K gives the index for the row just before r

kp1 = k + 1;      % K+1 gives the index for the row just after r

r = r - k;        % R is the ratio between the K and K+1 rows

k(k==0)=1; kp1(kp1==n+1)=n;

ynp = (0.5-r).*xs(k)+(0.5+r).*xs(kp1)

%%% 内嵌函数 quantile 和 prctile

yp = quantile(x,p)

yp = prctile(x,p*100)

运行结果

xnp =

 126.0000  145.0000  159.5000  177.0000  212.0000

xnp =

 126.0000  145.0000  159.5000  177.0000  212.0000

ynp =

 128.1000  145.0000  159.5000  177.0000  212.0000

yp =

 128.1000  145.0000  159.5000  177.0000  212.0000

yp =

 128.1000  145.0000  159.5000  177.0000  212.0000