在 Matplotlib 中为 Boxplot 提供自定义四分位距

Question

Matplotlib 或 Seaborn 箱线图给出了第 25 个百分位数和第 75 个百分位数之间的四分位距。有没有办法为 Boxplot 提供自定义四分位距？我需要得到箱线图，使得四分位距介于 10% 和 90% 之间。在谷歌和其他来源上查找，开始了解在箱线图上获取自定义胡须，而不是自定义四分位距。希望能在这里得到一些有用的解决方案。

Answer 1

是的，可以在您想要的任何百分位数处绘制带有框边的箱线图。

习俗

对于箱线图，通常绘制数据的第 25 个和第 75 个百分位数。因此，您应该意识到背离这个约定会使您面临误导读者的风险。您还应该仔细考虑改变箱百分位数对异常值分类和箱线图的胡须意味着什么。

快速解决方案

速战速决（忽略任何影响晶须的位置）是计算，我们的愿望箱线图统计数据，改变的位置q1和q3，然后绘制ax.bxp：

import matplotlib.cbook as cbook
import matplotlib.pyplot as plt
import numpy as np

# Generate some random data to visualise
np.random.seed(2019)
data = np.random.normal(size=100)

stats = {}
# Compute the boxplot stats (as in the default matplotlib implementation)
stats['A'] = cbook.boxplot_stats(data, labels='A')[0]
stats['B'] = cbook.boxplot_stats(data, labels='B')[0]
stats['C'] = cbook.boxplot_stats(data, labels='C')[0]

# For box A compute the 1st and 99th percentiles
stats['A']['q1'], stats['A']['q3'] = np.percentile(data, [1, 99])
# For box B compute the 10th and 90th percentiles
stats['B']['q1'], stats['B']['q3'] = np.percentile(data, [10, 90])
# For box C compute the 25th and 75th percentiles (matplotlib default)
stats['C']['q1'], stats['C']['q3'] = np.percentile(data, [25, 75])

fig, ax = plt.subplots(1, 1)
# Plot boxplots from our computed statistics
ax.bxp([stats['A'], stats['B'], stats['C']], positions=range(3))

然而，查看产生的情节，我们看到改变q1和q3保持胡须不变可能不是一个明智的想法。你可以通过重新计算来解决这个问题，例如。stats['A']['iqr']和晶须位置stats['A']['whishi']和stats['A']['whislo']。

更完整的解决方案

查看 matplotlib 的源代码，我们发现 matplotlib 用于matplotlib.cbook.boxplot_stats计算箱线图中使用的统计数据。

在里面boxplot_stats我们找到了代码q1, med, q3 = np.percentile(x, [25, 50, 75])。这是我们可以更改以更改绘制的百分位数的线。

因此，一个潜在的解决方案是根据我们的需要制作副本matplotlib.cbook.boxplot_stats并对其进行更改。在这里，我调用函数my_boxplot_stats，并添加参数percents，可以很容易改变的位置q1和q3。

import itertools
from matplotlib.cbook import _reshape_2D
import matplotlib.pyplot as plt
import numpy as np

# Function adapted from matplotlib.cbook
def my_boxplot_stats(X, whis=1.5, bootstrap=None, labels=None,
                  autorange=False, percents=[25, 75]):

    def _bootstrap_median(data, N=5000):
        # determine 95% confidence intervals of the median
        M = len(data)
        percentiles = [2.5, 97.5]

        bs_index = np.random.randint(M, size=(N, M))
        bsData = data[bs_index]
        estimate = np.median(bsData, axis=1, overwrite_input=True)

        CI = np.percentile(estimate, percentiles)
        return CI

    def _compute_conf_interval(data, med, iqr, bootstrap):
        if bootstrap is not None:
            # Do a bootstrap estimate of notch locations.
            # get conf. intervals around median
            CI = _bootstrap_median(data, N=bootstrap)
            notch_min = CI[0]
            notch_max = CI[1]
        else:

            N = len(data)
            notch_min = med - 1.57 * iqr / np.sqrt(N)
            notch_max = med + 1.57 * iqr / np.sqrt(N)

        return notch_min, notch_max

    # output is a list of dicts
    bxpstats = []

    # convert X to a list of lists
    X = _reshape_2D(X, "X")

    ncols = len(X)
    if labels is None:
        labels = itertools.repeat(None)
    elif len(labels) != ncols:
        raise ValueError("Dimensions of labels and X must be compatible")

    input_whis = whis
    for ii, (x, label) in enumerate(zip(X, labels)):

        # empty dict
        stats = {}
        if label is not None:
            stats['label'] = label

        # restore whis to the input values in case it got changed in the loop
        whis = input_whis

        # note tricksyness, append up here and then mutate below
        bxpstats.append(stats)

        # if empty, bail
        if len(x) == 0:
            stats['fliers'] = np.array([])
            stats['mean'] = np.nan
            stats['med'] = np.nan
            stats['q1'] = np.nan
            stats['q3'] = np.nan
            stats['cilo'] = np.nan
            stats['cihi'] = np.nan
            stats['whislo'] = np.nan
            stats['whishi'] = np.nan
            stats['med'] = np.nan
            continue

        # up-convert to an array, just to be safe
        x = np.asarray(x)

        # arithmetic mean
        stats['mean'] = np.mean(x)

        # median
        med = np.percentile(x, 50)
        ## Altered line
        q1, q3 = np.percentile(x, (percents[0], percents[1]))

        # interquartile range
        stats['iqr'] = q3 - q1
        if stats['iqr'] == 0 and autorange:
            whis = 'range'

        # conf. interval around median
        stats['cilo'], stats['cihi'] = _compute_conf_interval(
            x, med, stats['iqr'], bootstrap
        )

        # lowest/highest non-outliers
        if np.isscalar(whis):
            if np.isreal(whis):
                loval = q1 - whis * stats['iqr']
                hival = q3 + whis * stats['iqr']
            elif whis in ['range', 'limit', 'limits', 'min/max']:
                loval = np.min(x)
                hival = np.max(x)
            else:
                raise ValueError('whis must be a float, valid string, or list '
                                 'of percentiles')
        else:
            loval = np.percentile(x, whis[0])
            hival = np.percentile(x, whis[1])

        # get high extreme
        wiskhi = np.compress(x <= hival, x)
        if len(wiskhi) == 0 or np.max(wiskhi) < q3:
            stats['whishi'] = q3
        else:
            stats['whishi'] = np.max(wiskhi)

        # get low extreme
        wisklo = np.compress(x >= loval, x)
        if len(wisklo) == 0 or np.min(wisklo) > q1:
            stats['whislo'] = q1
        else:
            stats['whislo'] = np.min(wisklo)

        # compute a single array of outliers
        stats['fliers'] = np.hstack([
            np.compress(x < stats['whislo'], x),
            np.compress(x > stats['whishi'], x)
        ])

        # add in the remaining stats
        stats['q1'], stats['med'], stats['q3'] = q1, med, q3

    return bxpstats

有了这个，我们可以计算我们的统计数据，然后用 绘制plt.bxp。

# Generate some random data to visualise
np.random.seed(2019)
data = np.random.normal(size=100)

stats = {}

# Compute the boxplot stats with our desired percentiles
stats['A'] = my_boxplot_stats(data, labels='A', percents=[1, 99])[0]
stats['B'] = my_boxplot_stats(data, labels='B', percents=[10, 90])[0]
stats['C'] = my_boxplot_stats(data, labels='C', percents=[25, 75])[0]

fig, ax = plt.subplots(1, 1)
# Plot boxplots from our computed statistics
ax.bxp([stats['A'], stats['B'], stats['C']], positions=range(3))

看到使用此解决方案，根据我们选择的百分位数在我们的函数中调整胡须。：