三分位数的求解： SAS , R, Matlab 均不一致

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一串数字：1 1 1 2 3 3 6 6 6 6  8 8
求其三分位数，发现 SAS , R, Matlab给出的结果均不一样。
难道各软件的算法不同？

1. SAS


2. R



3. Matlab


附SAS Code:

1. data tmp;
   
2.   input w@@;
   
3. datalines;
   
4. 1 1 1 2 3 3 6 6 6 6  8 8
   
5. ;
   
6. run;
   
7. 
   
8. proc univariate data=tmp;
   
9.         var w;
   
10.         output out=pct pctlpts=33.3333  66.6666 pctlpre=p;
    
11. run;
    
12. 
    
13. proc print data=pct;
    
14. run;

复制代码

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关键词：MATLAB matla atlab Mat Atl 软件

33.3333 和66.6666应该还不足以让SAS明白我们想要的是3分位数。

data tmp;
  input w@@;
datalines;
1 1 1 2 3 3 6 6 7 7 8 8
;
run;
%let p33=%sysevalf(100/3);
%let p66=%sysevalf(200/3);


proc univariate data=tmp;
        var w;
       output out=pct pctlpts=&p33  &p66 pctlpre=p;
run;

proc print data=pct;
run;

其他能够影响到结果的就是percentile的计算方法了。SAS里是PCTLDEF=这个选项

pobel 发表于 2015-1-21 08:31
33.3333 和66.6666应该还不足以让SAS明白我们想要的是3分位数。

data tmp;

多谢pobel兄。

好久不见啊，论坛的时代好像过去了，大家都很少上来了。

我后来又查了下R 的help,发现有9种算法，第三种是SAS的算法。



types
quantile returns estimates of underlying distribution quantiles based on one or two order statistics from the supplied elements in x at probabilities in probs. One of the nine quantile algorithms discussed in Hyndman and Fan (1996), selected by type, is employed.
All sample quantiles are defined as weighted averages of consecutive order statistics. Sample quantiles of type i are defined by:

Q(p) = (1 - γ) x[j] + γ x[j+1],

where 1 ≤ i ≤ 9, (j-m)/n ≤ p < (j-m+1)/n, x[j] is the jth order statistic, n is the sample size, the value of γ is a function of j = floor(np + m) and g = np + m - j, and m is a constant determined by the sample quantile type.

Discontinuous sample quantile types 1, 2, and 3
For types 1, 2 and 3, Q(p) is a discontinuous function of p, with m = 0 when i = 1 and i = 2, and m = -1/2 when i = 3.

Type 1
Inverse of empirical distribution function. γ = 0 if g = 0, and 1 otherwise.

Type 2
Similar to type 1 but with averaging at discontinuities. γ = 0.5 if g = 0, and 1 otherwise.

Type 3
SAS definition: nearest even order statistic. γ = 0 if g = 0 and j is even, and 1 otherwise.

Continuous sample quantile types 4 through 9
For types 4 through 9, Q(p) is a continuous function of p, with gamma = g and m given below. The sample quantiles can be obtained equivalently by linear interpolation between the points(p[k],x[k]) where x[k] is the kth order statistic. Specific expressions for p[k] are given below.

Type 4m = 0. p[k] = k / n. That is, linear interpolation of the empirical cdf.

Type 5m = 1/2. p[k] = (k - 0.5) / n. That is a piecewise linear function where the knots are the values midway through the steps of the empirical cdf. This is popular amongst hydrologists.

Type 6
m = p. p[k] = k / (n + 1). Thus p[k] = E[F(x[k])]. This is used by Minitab and by SPSS.

Type 7
m = 1-p. p[k] = (k - 1) / (n - 1). In this case, p[k] = mode[F(x[k])]. This is used by S.

Type 8
m = (p+1)/3. p[k] = (k - 1/3) / (n + 1/3). Then p[k] =~ median[F(x[k])]. The resulting quantile estimates are approximately median-unbiased regardless of the distribution of x.

Type 9
m = p/4 + 3/8. p[k] = (k - 3/8) / (n + 1/4). The resulting quantile estimates are approximately unbiased for the expected order statistics if x is normally distributed.
Further details are provided in Hyndman and Fan (1996) who recommended type 8. The default method is type 7, as used by S and by R < 2.0.0.