一种更快的方法，基于扁平数组的 * 扩展 *：

df['std'] = (pd.Series(df.values.ravel()).expanding(3)
             .std(ddof=0).dropna()[::3].values)

a  b  c       std
day                   
1    2  2  8  2.828427
2    1  2  2  2.339278
3    7  2  3  2.346524
4    2  9  7  2.782635
5    4  6  4  2.542090

执行时间比较：

In [223]: %timeit pd.Series(df.values.ravel()).expanding(3).std(ddof=0).dropna()[::3].values
242 µs ± 2.56 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

In [224]: %timeit df.stack().expanding().std(ddof=0).groupby(level=0).last()
664 µs ± 17 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

In [225]: %timeit df.apply(lambda x: np.std(df.loc[:x.name].values), axis=1)
617 µs ± 15.3 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

In [226]: %timeit df.stack().expanding().std(ddof=0)[:, 'c']
427 µs ± 1.78 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

一种方法是stack + expanding + std + index每三个值，但这意味着你也计算中间体的std：

df["std"] = df.stack().expanding().std(ddof=0)[:, 'c']

df：

a  b  c       std
day
1    2  2  8  2.828427
2    1  2  2  2.339278
3    7  2  3  2.346524
4    2  9  7  2.782635
5    4  6  4  2.542090

试试这个：

df = pd.DataFrame({'a': [2, 1, 7, 2, 4],
                   'b': [2, 2, 2, 9, 6],
                   'c': [8, 2, 3, 7, 4]},
                  index=[1, 2, 3, 4, 5])
df['std'] = df.apply(lambda x: np.std(df.loc[:x.name].values), axis=1)

输出：

a   b   c   std
1   2   2   8   2.828427
2   1   2   2   2.339278
3   7   2   3   2.346524
4   2   9   7   2.782635
5   4   6   4   2.542090

如果数据中有NaN，示例也应该这样。

示例

data = {'a': {1: 2, 2: 1, 3: 7, 4: 2, 5: 4},
 'b': {1: 2, 2: 2, 3: 2, 4: 9, 5: 6},
 'c': {1: 8.0, 2: 2.0, 3: None, 4: 7.0, 5: 4.0}}
df = pd.DataFrame(data).rename_axis('day')

df

a   b   c
day         
1   2   2   8.0
2   1   2   2.0
3   7   2   NaN
4   2   9   7.0
5   4   6   4.0

编码

df['std'] = df.stack().expanding().std(ddof=0).groupby(level=0).last()

df

a   b   c   std
day             
1   2   2   8.0 2.828427
2   1   2   2.0 2.339278
3   7   2   NaN 2.487469
4   2   9   7.0 2.891995
5   4   6   4.0 2.614715