z-score算法原理参考网址
https://blog.csdn.net/m0_59596937/article/details/128378641

具体实现代码如下：

import numpy as np

class ZScoreOutlierDetector:
    def __init__(self, threshold=3):
        """构造函数"""
        self.threshold = threshold  # Z-score阈值，默认为3
        self.x_mean = None          # X坐标的均值
        self.x_std = None           # X坐标的标准差
        self.y_mean = None          # Y坐标的均值
        self.y_std = None           # Y坐标的标准差

    def fit(self, points):
        """根据样本数据计算各维度(x,y维度)的均值和标准差"""
        points = np.array(points)
        x = points[:, 0]#:表示选择所有行，0表示选择第0列(通常是x坐标)
        y = points[:, 1]
        self.x_mean = np.mean(x)
        self.x_std = np.std(x)
        self.y_mean = np.mean(y)
        self.y_std = np.std(y)

    def _calc_z_score(self, val, mean, std):
        """计算单个维度的Z-score，并且处理标准差为0的情况"""
        if std == 0:
            # 如果样本数据全相同，则当前值不同时视为无限大Z-score（即离群点）
            return float('inf') if val != mean else 0#python三元运算符
            #float('inf')表示无穷大
        return (val - mean) / std

    def is_outlier(self, point):
        """判断给定点是否为离群点"""
        x_z = self._calc_z_score(point[0], self.x_mean, self.x_std)
        y_z = self._calc_z_score(point[1], self.y_mean, self.y_std)
        # 任一维度超过阈值则视为离群点
        return abs(x_z) > self.threshold or abs(y_z) > self.threshold

# 示例用法
if __name__ == "__main__":
    # 样本数据
    sample_points = [
        (1.0, 2.0),
        (1.5, 3.0),
        (1.2, 2.5),
        (1.8, 3.2),
        (0.9, 2.1)
    ]

    # 初始化检测器并拟合数据
    detector = ZScoreOutlierDetector(threshold=3)
    detector.fit(sample_points)

    # 待检测点
    test_point = (5.0, 4.0)
    result = detector.is_outlier(test_point)

    print(f"检测点 {test_point} 是否为离群点：{result}")