Update distribution.py

.idea/.gitignore

@@ -6,3 +6,5 @@
 # Datasource local storage ignored files
 /dataSources/
 /dataSources.local.xml
+# GitHub Copilot persisted chat sessions
+/copilot/chatSessions

.idea/casio-calculator.iml

@@ -1,7 +1,9 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <module type="PYTHON_MODULE" version="4">
   <component name="NewModuleRootManager">
-    <content url="file://$MODULE_DIR$" />
+    <content url="file://$MODULE_DIR$">
+      <excludeFolder url="file://$MODULE_DIR$/.idea/copilot/chatSessions" />
+    </content>
     <orderEntry type="jdk" jdkName="Pipenv (casio-calculator)" jdkType="Python SDK" />
     <orderEntry type="sourceFolder" forTests="false" />
   </component>

Pipfile

@@ -9,4 +9,3 @@ name = "pypi"
 
 [requires]
 python_version = "3.11"
-python_full_version = "3.11.7"

Pipfile.lock

@@ -1,11 +1,10 @@
 {
     "_meta": {
         "hash": {
-            "sha256": "bc82cd27f07d4e24b750064464bbc233a141778868b9a387125705e2d4e8a830"
+            "sha256": "ed6d5d614626ae28e274e453164affb26694755170ccab3aa5866f093d51d3e4"
         },
         "pipfile-spec": 6,
         "requires": {
-            "python_full_version": "3.11.7",
             "python_version": "3.11"
         },
         "sources": [

distribution.py

@@ -1,4 +1,5 @@
 import math
+import statistics
 
 
 def factorial(n):
@@ -371,14 +372,117 @@ def pd_gt(x, l):
     return 1 - pd_leq(x, l)
 
 
+def sample_mean_e(u):
+    """
+    Computes the expected value of the sample mean.
+    :param u: The population mean.
+    :return: Returns the expected value of the sample mean.
+    """
+    return u
+
+
+def sample_mean_std(u, n):
+    """
+    Computes the standard deviation of the sample mean.
+    :param u: The population mean.
+    :param n: The sample size.
+    :return: Returns the standard deviation of the sample mean.
+    """
+    return u / n ** 0.5
+
+
+def sample_mean_var(u, n):
+    """
+    Computes the variance of the sample mean.
+    :param u: The population mean.
+    :param n: The sample size.
+    :return: Returns the variance of the sample mean.
+    """
+    return (sample_mean_std(u, n) ** 2) / n
+
+
+def z_score(x, u, s):
+    """
+    Computes the z-score of a sample.
+    :param x: The sample mean.
+    :param u: The population mean.
+    :param s: The standard deviation of the sample mean.
+    :return: Returns the z-score of the sample.
+    """
+    return (x - u) / s
+
+
+def z_to_p(z):
+    """
+    Computes the probability of a z-score.
+    :param z: The z-score.
+    :return: Returns the probability of the z-score.
+    """
+    nd = statistics.NormalDist()
+    return nd.cdf(z)
+
+
+def p_to_z(p):
+    """
+    Computes the z-score of a probability.
+    :param p: The probability.
+    :return: Returns the z-score of the probability.
+    """
+    nd = statistics.NormalDist()
+    return nd.inv_cdf(p)
+
+
+def gamma(u, n):
+    """
+    Computes the gamma of a sample.
+    :param u: The population mean.
+    :param n: The sample size.
+    :return: Returns the gamma of the sample.
+    """
+    return sample_mean_var(u, n) / sample_mean_e(u)
+
+
+def alpha(u, n):
+    """
+    Computes the alpha of a sample.
+    :param u: The population mean.
+    :param n: The sample size.
+    :return: Returns the alpha of the sample.
+    """
+    return sample_mean_e(u) / gamma(u, n)
+
+
+def margin_of_error(a, s, n):
+    """
+    Computes the margin of error of a sample.
+    :param a: The alpha of the sample.
+    :param s: The standard deviation of the sample mean.
+    :param n: The sample size.
+    :return: Returns the margin of error of the sample.
+    """
+    return abs((p_to_z(a / 2)) * (s / (n ** 0.5)))
+
+
+def confidence_interval(x, a, s, n):
+    """
+    Computes the confidence interval of a sample.
+    :param x: The sample mean.
+    :param a: The alpha of the sample.
+    :param s: The standard deviation of the sample mean.
+    :param n: The sample size.
+    :return: Returns the confidence interval of the sample.
+    """
+    return x - margin_of_error(a, s, n), x + margin_of_error(a, s, n)
+
+
 def man():
     """
     Prints the manual for the module.
     """
-	seperator = "-" * 20
+    separator = "-" * 20
     print("This module contains functions for computing the total probability of events.")
     print("The functions are:")
-	print(seperator)
+    print(separator)
     print("Binomial Distribution")
     print("bnd(x, n, p)")
     print("bnd_mean(n, p)")
@@ -388,7 +492,7 @@ def man():
     print("bnd_lt(x, n, p)")
     print("bnd_geq(x, n, p)")
     print("bnd_gt(x, n, p)")
-	print(seperator)
+    print(separator)
     print("Geometric Distribution")
     print("gd(x, p, q)")
     print("gd_mean(p)")
@@ -398,7 +502,7 @@ def man():
     print("gd_lt(x, p, q)")
     print("gd_geq(x, p, q)")
     print("gd_gt(x, p, q)")
-	print(seperator)
+    print(separator)
     print("Hyper Geometric Distribution")
     print("hgd(x, N, n, k)")
     print("hgd_mean(N, n, k)")
@@ -408,7 +512,7 @@ def man():
     print("hgd_lt(x, N, n, k)")
     print("hgd_geq(x, N, n, k)")
     print("hgd_gt(x, N, n, k)")
-	print(seperator)
+    print(separator)
     print("Poisson Distribution")
     print("pd(x, l)")
     print("pd_mean(l)")
@@ -418,3 +522,15 @@ def man():
     print("pd_lt(x, l)")
     print("pd_geq(x, l)")
     print("pd_gt(x, l)")
+    print(separator)
+    print("Sample Mean")
+    print("sample_mean_e(u)")
+    print("sample_mean_std(u, n)")
+    print("sample_mean_var(u, n)")
+    print("z_score(x, u, s)")
+    print("z_to_p(z)")
+    print("p_to_z(p)")
+    print("gamma(u, n)")
+    print("alpha(u, n)")
+    print("margin_of_error(a, s, n)")
+    print("confidence_interval(x, a, s, n)")