From cdc19c0509f88189f55d8c3cf3d8bfdffe5b8a40 Mon Sep 17 00:00:00 2001
From: Isaac Shoebottom <ir.shoebottom@gmail.com>
Date: Mon, 22 Apr 2024 13:16:50 -0300
Subject: [PATCH] Add some cdf functions from std lib

---
 cdf.py          | 79 +++++++++++++++++++++++++++++++++++++++++++++++++
 distribution.py |  9 +++---
 2 files changed, 83 insertions(+), 5 deletions(-)
 create mode 100644 cdf.py

diff --git a/cdf.py b/cdf.py
new file mode 100644
index 0000000..bb8a7f8
--- /dev/null
+++ b/cdf.py
@@ -0,0 +1,79 @@
+import math
+
+
+def normal_dist_cdf(x, mu=0.0, sigma=1.0):
+    return 0.5 * (1.0 + math.erf((x - mu) / (sigma * (2 ** 0.5))))
+
+
+def normal_dist_inv_cdf(p, mu=0.0, sigma=1.0):
+    # There is no closed-form solution to the inverse CDF for the normal
+    # distribution, so we use a rational approximation instead:
+    # Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the
+    # Normal Distribution".  Applied Statistics. Blackwell Publishing. 37
+    # (3): 477–484. doi:10.2307/2347330. JSTOR 2347330.
+    q = p - 0.5
+    if math.fabs(q) <= 0.425:
+        r = 0.180625 - q * q
+        # Hash sum: 55.88319_28806_14901_4439
+        num = (((((((2.50908_09287_30122_6727e+3 * r +
+                     3.34305_75583_58812_8105e+4) * r +
+                    6.72657_70927_00870_0853e+4) * r +
+                   4.59219_53931_54987_1457e+4) * r +
+                  1.37316_93765_50946_1125e+4) * r +
+                 1.97159_09503_06551_4427e+3) * r +
+                1.33141_66789_17843_7745e+2) * r +
+               3.38713_28727_96366_6080e+0) * q
+        den = (((((((5.22649_52788_52854_5610e+3 * r +
+                     2.87290_85735_72194_2674e+4) * r +
+                    3.93078_95800_09271_0610e+4) * r +
+                   2.12137_94301_58659_5867e+4) * r +
+                  5.39419_60214_24751_1077e+3) * r +
+                 6.87187_00749_20579_0830e+2) * r +
+                4.23133_30701_60091_1252e+1) * r +
+               1.0)
+        x = num / den
+        return mu + (x * sigma)
+    r = p if q <= 0.0 else 1.0 - p
+    r = math.sqrt(-math.log(r))
+    if r <= 5.0:
+        r = r - 1.6
+        # Hash sum: 49.33206_50330_16102_89036
+        num = (((((((7.74545_01427_83414_07640e-4 * r +
+                     2.27238_44989_26918_45833e-2) * r +
+                    2.41780_72517_74506_11770e-1) * r +
+                   1.27045_82524_52368_38258e+0) * r +
+                  3.64784_83247_63204_60504e+0) * r +
+                 5.76949_72214_60691_40550e+0) * r +
+                4.63033_78461_56545_29590e+0) * r +
+               1.42343_71107_49683_57734e+0)
+        den = (((((((1.05075_00716_44416_84324e-9 * r +
+                     5.47593_80849_95344_94600e-4) * r +
+                    1.51986_66563_61645_71966e-2) * r +
+                   1.48103_97642_74800_74590e-1) * r +
+                  6.89767_33498_51000_04550e-1) * r +
+                 1.67638_48301_83803_84940e+0) * r +
+                2.05319_16266_37758_82187e+0) * r +
+               1.0)
+    else:
+        r = r - 5.0
+        # Hash sum: 47.52583_31754_92896_71629
+        num = (((((((2.01033_43992_92288_13265e-7 * r +
+                     2.71155_55687_43487_57815e-5) * r +
+                    1.24266_09473_88078_43860e-3) * r +
+                   2.65321_89526_57612_30930e-2) * r +
+                  2.96560_57182_85048_91230e-1) * r +
+                 1.78482_65399_17291_33580e+0) * r +
+                5.46378_49111_64114_36990e+0) * r +
+               6.65790_46435_01103_77720e+0)
+        den = (((((((2.04426_31033_89939_78564e-15 * r +
+                     1.42151_17583_16445_88870e-7) * r +
+                    1.84631_83175_10054_68180e-5) * r +
+                   7.86869_13114_56132_59100e-4) * r +
+                  1.48753_61290_85061_48525e-2) * r +
+                 1.36929_88092_27358_05310e-1) * r +
+                5.99832_20655_58879_37690e-1) * r +
+               1.0)
+    x = num / den
+    if q < 0.0:
+        x = -x
+    return mu + (x * sigma)
diff --git a/distribution.py b/distribution.py
index 6b18bde..618b3dc 100644
--- a/distribution.py
+++ b/distribution.py
@@ -1,5 +1,5 @@
 import math
-import statistics
+import cdf
 
 
 def factorial(n):
@@ -418,8 +418,8 @@ def z_to_p(z):
     :param z: The z-score.
     :return: Returns the probability of the z-score.
     """
-    nd = statistics.NormalDist()
-    return nd.cdf(z)
+
+    return cdf.normal_dist_cdf(z)
 
 
 def p_to_z(p):
@@ -428,8 +428,7 @@ def p_to_z(p):
     :param p: The probability.
     :return: Returns the z-score of the probability.
     """
-    nd = statistics.NormalDist()
-    return nd.inv_cdf(p)
+    return cdf.normal_dist_inv_cdf(p)
 
 
 def gamma(u, n):