Added stats.py

stats.py

@@ -0,0 +1,53 @@
+########################################################################
+#
+# Various statistical functions.
+#
+########################################################################
+#
+# This file is part of FinanceOps:
+#
+# https://github.com/Hvass-Labs/FinanceOps
+#
+# Published under the MIT License. See the file LICENSE for details.
+#
+# Copyright 2021 by Magnus Erik Hvass Pedersen
+#
+########################################################################
+
+import numpy as np
+from scipy.stats import norm
+
+########################################################################
+
+
+def normal_prob_loss(mean, std):
+    """
+    Probability of loss for a normal distribution.
+
+    :param mean: Float with mean.
+    :param std: Float with standard deviation.
+    :return: Float with probability of loss.
+    """
+    return norm.cdf(0.0, loc=mean, scale=std)
+
+
+def normal_prob_less_than(mean1, std1, mean2, std2):
+    """
+    Probability that X1 < X2 for two independent and normal-distributed random
+    variables X1 and X2, where X1 ~ N(mean1, std1^2) and X2 ~ N(mean2, std2^2)
+
+    :param mean1: Float with mean for X1.
+    :param std1: Float with std.dev. for X1.
+    :param mean2: Float with mean for X2.
+    :param std2: Float with std.dev. for X2.
+    :return: Float with probability that X1 < X2.
+    """
+    # The difference of two normal random variables is also a random normal
+    # variable with the following mean and std.dev. so we can simply calculate
+    # the probability of that new random variable being less than zero.
+    mean = mean1 - mean2
+    std = np.sqrt(std1 ** 2 + std2 ** 2)
+    return norm.cdf(0.0, loc=mean, scale=std)
+
+
+########################################################################