写一段python马氏性检验的代码

以下是一段 Python 马氏性检验的代码：

import numpy as np
from scipy.stats import chi2

def mahalanobis_distance(x, mean, cov):
    x_minus_mean = x - mean
    inv_covmat = np.linalg.inv(cov)
    left_term = np.dot(x_minus_mean, inv_covmat)
    mahal = np.dot(left_term, x_minus_mean.T)
    return mahal

def mahalanobis_test(data, alpha):
    n = data.shape[0]
    p = data.shape[1]
    mean = np.mean(data, axis=0)
    cov = np.cov(data.T)
    distances = []
    for i in range(n):
        x = data[i]
        mahal = mahalanobis_distance(x, mean, cov)
        distances.append(mahal)
    distances = np.array(distances)
    threshold = chi2.ppf(1-alpha, p)
    outliers = np.where(distances > threshold)[0]
    return outliers

这段代码实现了马氏距离的计算和基于马氏距离的异常检测。给定一个数据集，我们首先计算数据集的均值和协方差矩阵，然后计算每个数据点与均值之间的马氏距离。最后，我们使用卡方分布来计算异常值的阈值，并将大于阈值的数据点标记为异常值。