Fix cdf on micropython

.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>

.idea/modules.xml

@@ -2,7 +2,7 @@
 <project version="4">
   <component name="ProjectModuleManager">
     <modules>
-      <module fileurl="file://$PROJECT_DIR$/.idea/Calculator.iml" filepath="$PROJECT_DIR$/.idea/Calculator.iml" />
+      <module fileurl="file://$PROJECT_DIR$/.idea/casio-calculator.iml" filepath="$PROJECT_DIR$/.idea/casio-calculator.iml" />
     </modules>
   </component>
 </project>

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": [

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 = (((((((2.5090809287301226727e+3 * r +
+                     3.3430575583588128105e+4) * r +
+                    6.7265770927008700853e+4) * r +
+                   4.5921953931549871457e+4) * r +
+                  1.3731693765509461125e+4) * r +
+                 1.9715909503065514427e+3) * r +
+                1.3314166789178437745e+2) * r +
+               3.3871328727963666080e+0) * q
+        den = (((((((5.2264952788528545610e+3 * r +
+                     2.8729085735721942674e+4) * r +
+                    3.9307895800092710610e+4) * r +
+                   2.1213794301586595867e+4) * r +
+                  5.3941960214247511077e+3) * r +
+                 6.8718700749205790830e+2) * r +
+                4.2313330701600911252e+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 = (((((((7.74545014278341407640e-4 * r +
+                     2.27238449892691845833e-2) * r +
+                    2.41780725177450611770e-1) * r +
+                   1.27045825245236838258e+0) * r +
+                  3.64784832476320460504e+0) * r +
+                 5.76949722146069140550e+0) * r +
+                4.63033784615654529590e+0) * r +
+               1.42343711074968357734e+0)
+        den = (((((((1.05075007164441684324e-9 * r +
+                     5.47593808499534494600e-4) * r +
+                    1.51986665636164571966e-2) * r +
+                   1.48103976427480074590e-1) * r +
+                  6.89767334985100004550e-1) * r +
+                 1.67638483018380384940e+0) * r +
+                2.05319162663775882187e+0) * r +
+               1.0)
+    else:
+        r = r - 5.0
+        # Hash sum: 47.52583317549289671629
+        num = (((((((2.01033439929228813265e-7 * r +
+                     2.71155556874348757815e-5) * r +
+                    1.24266094738807843860e-3) * r +
+                   2.65321895265761230930e-2) * r +
+                  2.96560571828504891230e-1) * r +
+                 1.78482653991729133580e+0) * r +
+                5.46378491116411436990e+0) * r +
+               6.65790464350110377720e+0)
+        den = (((((((2.04426310338993978564e-15 * r +
+                     1.42151175831644588870e-7) * r +
+                    1.84631831751005468180e-5) * r +
+                   7.86869131145613259100e-4) * r +
+                  1.48753612908506148525e-2) * r +
+                 1.36929880922735805310e-1) * r +
+                5.99832206555887937690e-1) * r +
+               1.0)
+    x = num / den
+    if q < 0.0:
+        x = -x
+    return mu + (x * sigma)

distribution.py

@@ -1,281 +1,535 @@
 import math
+import cdf
+
+
+def factorial(n):
+    """
+    Computes the factorial of a number.
+    :param n: The number to compute the factorial of.
+    :return: Returns the factorial of the number.
+    """
+    if n == 0:
+        return 1
+    for i in range(1, n):
+        n *= i
+    return n
+
+
+def combination(n, r):
+    """
+    Computes the combination of n choose r.
+    :param n: The number of items.
+    :param r: The number of items to choose.
+    :return: Returns the number of ways to choose r items from n items.
+    """
+    return factorial(n) / (factorial(r) * factorial(n - r))
 
 
 def bnd(x, n, p):
-	"""
+    """
-	Computes the binomial distribution.
+    Computes the binomial distribution.
-	:param x: Number of successes.
+    :param x: Number of successes.
-	:param n: Number of trials.
+    :param n: Number of trials.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:return: Returns the probability of getting x successes in n trials.
+    :return: Returns the probability of getting x successes in n trials.
-	"""
+    """
-	return math.comb(n, x) * p ** x * (1 - p) ** (n - x)
+    return combination(n, x) * p ** x * (1 - p) ** (n - x)
 
 
 def bnd_mean(n, p):
-	"""
+    """
-	Computes the mean of the binomial distribution.
+    Computes the mean of the binomial distribution.
-	:param n: Number of trials.
+    :param n: Number of trials.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:return: Returns the mean of the binomial distribution.
+    :return: Returns the mean of the binomial distribution.
-	"""
+    """
-	return n * p
+    return n * p
 
 
 def bnd_var(n, p):
-	"""
+    """
-	Computes the variance of the binomial distribution.
+    Computes the variance of the binomial distribution.
-	:param n: Number of trials.
+    :param n: Number of trials.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:return: Returns the variance of the binomial distribution.
+    :return: Returns the variance of the binomial distribution.
-	"""
+    """
-	return n * p * (1 - p)
+    return n * p * (1 - p)
 
 
 def bnd_std(n, p):
-	"""
+    """
-	Computes the standard deviation of the binomial distribution.
+    Computes the standard deviation of the binomial distribution.
-	:param n: Number of trials.
+    :param n: Number of trials.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:return: Returns the standard deviation of the binomial distribution.
+    :return: Returns the standard deviation of the binomial distribution.
-	"""
+    """
-	return bnd_var(n, p) ** 0.5
+    return bnd_var(n, p) ** 0.5
 
 
-def bnd_upto(x, n, p):
+def bnd_leq(x, n, p):
-	"""
+    """
-	Computes the cumulative probability of getting upto x successes in n trials.
+    Computes the cumulative probability less than or equal to x successes in n trials.
-	:param x: Number of successes.
+    :param x: Number of successes.
-	:param n: Number of trials.
+    :param n: Number of trials.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:return: Returns the cumulative probability of getting upto x successes in n trials.
+    :return: Returns the cumulative probability less than or equal to x successes in n trials.
-	"""
+    """
-	return sum(bnd(i, n, p) for i in range(x + 1))
+    return sum(bnd(i, n, p) for i in range(x + 1))
 
 
-def bnd_from(x, n, p):
+def bnd_lt(x, n, p):
-	"""
+    """
-	Computes the cumulative probability of getting from x successes in n trials.
+    Computes the cumulative probability less than x successes in n trials.
-	:param x: Number of successes.
+    :param x: Number of successes.
-	:param n: Number of trials.
+    :param n: Number of trials.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:return: Returns the cumulative probability of getting from x successes in n trials.
+    :return: Returns the cumulative probability less than x successes in n trials.
-	"""
+    """
-	return 1 - bnd_upto(x - 1, n, p)
+    return sum(bnd(i, n, p) for i in range(x))
+
+
+def bnd_geq(x, n, p):
+    """
+    Computes the cumulative probability greater than or equal to x successes in n trials.
+    :param x: Number of successes.
+    :param n: Number of trials.
+    :param p: Probability of success.
+    :return: Returns the cumulative probability greater than or equal to x successes in n trials.
+    """
+    return 1 - bnd_lt(x, n, p)
+
+
+def bnd_gt(x, n, p):
+    """
+    Computes the cumulative probability greater than x successes in n trials.
+    :param x: Number of successes.
+    :param n: Number of trials.
+    :param p: Probability of success.
+    :return: Returns the cumulative probability greater than x successes in n trials.
+    """
+    return 1 - bnd_leq(x, n, p)
 
 
 def gd(x, p, q=None):
-	"""
+    """
-	Computes the geometric distribution.
+    Computes the geometric distribution.
-	:param x: Number of trials until the first success.
+    :param x: Number of trials until the first success.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:param q: Probability of failure.
+    :param q: Probability of failure.
-	:return: Returns the probability of getting the first success on the xth trial.
+    :return: Returns the probability of getting the first success on the xth trial.
-	"""
+    """
-	if q is None:
+    if q is None:
-		q = 1 - p
+        q = 1 - p
-	return q ** (x - 1) * p
+    return q ** (x - 1) * p
 
 
 def gd_mean(p):
-	"""
+    """
-	Computes the mean of the geometric distribution.
+    Computes the mean of the geometric distribution.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:return: Returns the mean of the geometric distribution.
+    :return: Returns the mean of the geometric distribution.
-	"""
+    """
-	return 1 / p
+    return 1 / p
 
 
 def gd_var(p):
-	"""
+    """
-	Computes the variance of the geometric distribution.
+    Computes the variance of the geometric distribution.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:return: Returns the variance of the geometric distribution.
+    :return: Returns the variance of the geometric distribution.
-	"""
+    """
-	return (1 - p) / p ** 2
+    return (1 - p) / p ** 2
 
 
 def gd_std(p):
-	"""
+    """
-	Computes the standard deviation of the geometric distribution.
+    Computes the standard deviation of the geometric distribution.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:return: Returns the standard deviation of the geometric distribution.
+    :return: Returns the standard deviation of the geometric distribution.
-	"""
+    """
-	return gd_var(p) ** 0.5
+    return gd_var(p) ** 0.5
 
 
-def gd_upto(x, p):
+def gd_leq(x, p, q=None):
-	"""
+    """
-	Computes the cumulative probability of getting upto x trials until the first success.
+    Computes the cumulative probability of getting upto x trials until the first success.
-	:param x: Number of trials until the first success.
+    :param x: Number of trials until the first success.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:return: Returns the cumulative probability of getting upto x trials until the first success.
+    :param q: Probability of failure.
-	"""
+    :return: Returns the cumulative probability of getting upto x trials until the first success.
-	return sum(gd(i, p) for i in range(1, x + 1))
+    """
+    if q is not None:
+        return sum(gd(i, p, q) for i in range(1, x + 1))
+    return sum(gd(i, p) for i in range(1, x + 1))
 
 
-def gd_from(x, p):
+def gd_lt(x, p, q=None):
-	"""
+    """
-	Computes the cumulative probability of getting from x trials until the first success.
+    Computes the cumulative probability of getting less than x trials until the first success.
-	:param x: Number of trials until the first success.
+    :param x: Number of trials until the first success.
-	:param p: Probability of success.
+    :param p: Probability of success.
-	:return: Returns the cumulative probability of getting from x trials until the first success.
+    :param q: Probability of failure.
-	"""
+    :return: Returns the cumulative probability of getting less than x trials until the first success.
-	return 1 - gd_upto(x - 1, p)
+    """
+    if q is not None:
+        return sum(gd(i, p, q) for i in range(1, x))
+    return sum(gd(i, p) for i in range(1, x))
+
+
+def gd_geq(x, p, q=None):
+    """
+    Computes the cumulative probability of getting from x trials until the first success.
+    :param x: Number of trials until the first success.
+    :param p: Probability of success.
+    :param q: Probability of failure.
+    :return: Returns the cumulative probability of getting from x trials until the first success.
+    """
+    if q is not None:
+        return 1 - gd_lt(x, p, q)
+    return 1 - gd_leq(x, p)
+
+
+def gd_gt(x, p, q=None):
+    """
+    Computes the cumulative probability of getting from x trials until the first success.
+    :param x: Number of trials until the first success.
+    :param p: Probability of success.
+    :param q: Probability of failure.
+    :return: Returns the cumulative probability of getting from x trials until the first success.
+    """
+    if q is not None:
+        return 1 - gd_leq(x, p, q)
+    return 1 - gd_leq(x, p)
 
 
 def hgd(x, N, n, k):
-	"""
+    """
-	Computes the hyper geometric distribution.
+    Computes the hyper geometric distribution.
-	:param x: Number of successes in the sample.
+    :param x: Number of successes in the sample.
-	:param N: Number of items in the population.
+    :param N: Number of items in the population.
-	:param n: Number of draws.
+    :param n: Number of draws.
-	:param k: Number of successes in the population.
+    :param k: Number of successes in the population.
-	:return: Returns the probability of getting x successes in n draws from a population of size N with k successes.
+    :return: Returns the probability of getting x successes in n draws from a population of size N with k successes.
-	"""
+    """
-	return (math.comb(k, x) * math.comb(N - k, n - x)) / math.comb(N, n)
+    return (combination(k, x) * combination(N - k, n - x)) / combination(N, n)
 
 
 def hgd_mean(N, n, k):
-	"""
+    """
-	Computes the mean of the hyper geometric distribution.
+    Computes the mean of the hyper geometric distribution.
-	:param N: Number of items in the population.
+    :param N: Number of items in the population.
-	:param n: Number of draws.
+    :param n: Number of draws.
-	:param k: Number of successes in the population.
+    :param k: Number of successes in the population.
-	:return: Returns the mean of the hyper geometric distribution.
+    :return: Returns the mean of the hyper geometric distribution.
-	"""
+    """
-	return n * (k / N)
+    return n * (k / N)
 
 
 def hgd_var(N, n, k):
-	"""
+    """
-	Computes the variance of the hyper geometric distribution.
+    Computes the variance of the hyper geometric distribution.
-	:param N: Number of items in the population.
+    :param N: Number of items in the population.
-	:param n: Number of draws.
+    :param n: Number of draws.
-	:param k: Number of successes in the population.
+    :param k: Number of successes in the population.
-	:return: Returns the variance of the hyper geometric distribution.
+    :return: Returns the variance of the hyper geometric distribution.
-	"""
+    """
-	return (n * k * (N - k) * (N - n)) / (N ** 2 * (N - 1))
+    return (n * k * (N - k) * (N - n)) / (N ** 2 * (N - 1))
 
 
 def hgd_std(N, n, k):
-	"""
+    """
-	Computes the standard deviation of the hyper geometric distribution.
+    Computes the standard deviation of the hyper geometric distribution.
-	:param N: Number of items in the population.
+    :param N: Number of items in the population.
-	:param n: Number of draws.
+    :param n: Number of draws.
-	:param k: Number of successes in the population.
+    :param k: Number of successes in the population.
-	:return: Returns the standard deviation of the hyper geometric distribution.
+    :return: Returns the standard deviation of the hyper geometric distribution.
-	"""
+    """
-	return hgd_var(N, n, k) ** 0.5
+    return hgd_var(N, n, k) ** 0.5
 
 
-def hgd_upto(x, N, n, k):
+def hgd_leq(x, N, n, k):
-	"""
+    """
-	Computes the cumulative probability of getting upto x successes in n draws from a population of size N with k successes.
+    Computes the cumulative probability of getting upto x successes in n draws from a population of size N with k successes.
-	:param x: Number of successes in the sample.
+    :param x: Number of successes in the sample.
-	:param N: Number of items in the population.
+    :param N: Number of items in the population.
-	:param n: Number of draws.
+    :param n: Number of draws.
-	:param k: Number of successes in the population.
+    :param k: Number of successes in the population.
-	:return: Returns the cumulative probability of getting upto x successes in n draws from a population of size N with k successes.
+    :return: Returns the cumulative probability of getting upto x successes in n draws from a population of size N with k successes.
-	"""
+    """
-	return sum(hgd(i, N, n, k) for i in range(x + 1))
+    return sum(hgd(i, N, n, k) for i in range(x + 1))
 
 
-def hgd_from(x, N, n, k):
+def hgd_lt(x, N, n, k):
-	"""
+    """
-	Computes the cumulative probability of getting from x successes in n draws from a population of size N with k successes.
+    Computes the cumulative probability of getting less than x successes in n draws from a population of size N with k successes.
-	:param x: Number of successes in the sample.
+    :param x: Number of successes in the sample.
-	:param N: Number of items in the population.
+    :param N: Number of items in the population.
-	:param n: Number of draws.
+    :param n: Number of draws.
-	:param k: Number of successes in the population.
+    :param k: Number of successes in the population.
-	:return: Returns the cumulative probability of getting from x successes in n draws from a population of size N with k successes.
+    :return: Returns the cumulative probability of getting less than x successes in n draws from a population of size N with k successes.
-	"""
+    """
-	return 1 - hgd_upto(x - 1, N, n, k)
+    return sum(hgd(i, N, n, k) for i in range(x))
+
+
+def hgd_geq(x, N, n, k):
+    """
+    Computes the cumulative probability of getting from x successes in n draws from a population of size N with k successes.
+    :param x: Number of successes in the sample.
+    :param N: Number of items in the population.
+    :param n: Number of draws.
+    :param k: Number of successes in the population.
+    :return: Returns the cumulative probability of getting from x successes in n draws from a population of size N with k successes.
+    """
+    return 1 - hgd_lt(x, N, n, k)
+
+
+def hgd_gt(x, N, n, k):
+    """
+    Computes the cumulative probability of getting from x successes in n draws from a population of size N with k successes.
+    :param x: Number of successes in the sample.
+    :param N: Number of items in the population.
+    :param n: Number of draws.
+    :param k: Number of successes in the population.
+    :return: Returns the cumulative probability of getting from x successes in n draws from a population of size N with k successes.
+    """
+    return 1 - hgd_leq(x, N, n, k)
 
 
 def pd(x, l):
-	"""
+    """
-	Computes the poisson distribution.
+    Computes the poisson distribution.
-	:param x: Number of occurrences.
+    :param x: Number of occurrences.
-	:param l: Average number of occurrences.
+    :param l: Average number of occurrences.
-	:return: Returns the probability of getting x occurrences.
+    :return: Returns the probability of getting x occurrences.
-	"""
+    """
-	return (l ** x * math.e ** -l) / math.factorial(x)
+    return (l ** x * math.e ** -l) / factorial(x)
 
 
 def pd_mean(l):
-	"""
+    """
-	Computes the mean of the poisson distribution.
+    Computes the mean of the poisson distribution.
-	:param l: Average number of occurrences.
+    :param l: Average number of occurrences.
-	:return: Returns the mean of the poisson distribution.
+    :return: Returns the mean of the poisson distribution.
-	"""
+    """
-	return l
+    return l
 
 
 def pd_var(l):
-	"""
+    """
-	Computes the variance of the poisson distribution.
+    Computes the variance of the poisson distribution.
-	:param l: Average number of occurrences.
+    :param l: Average number of occurrences.
-	:return: Returns the variance of the poisson distribution.
+    :return: Returns the variance of the poisson distribution.
-	"""
+    """
-	return l
+    return l
 
 
 def pd_std(l):
-	"""
+    """
-	Computes the standard deviation of the poisson distribution.
+    Computes the standard deviation of the poisson distribution.
-	:param l: Average number of occurrences.
+    :param l: Average number of occurrences.
-	:return: Returns the standard deviation of the poisson distribution.
+    :return: Returns the standard deviation of the poisson distribution.
-	"""
+    """
-	return l ** 0.5
+    return l ** 0.5
 
 
-def pd_upto(x, l):
+def pd_leq(x, l):
-	"""
+    """
-	Computes the cumulative probability of getting upto x occurrences.
+    Computes the cumulative probability of getting upto x occurrences.
-	:param x: Number of occurrences.
+    :param x: Number of occurrences.
-	:param l: Average number of occurrences.
+    :param l: Average number of occurrences.
-	:return: Returns the cumulative probability of getting upto x occurrences.
+    :return: Returns the cumulative probability of getting upto x occurrences.
-	"""
+    """
-	return sum(pd(i, l) for i in range(x + 1))
+    return sum(pd(i, l) for i in range(x + 1))
 
 
-def pd_from(x, l):
+def pd_lt(x, l):
-	"""
+    """
-	Computes the cumulative probability of getting from x occurrences.
+    Computes the cumulative probability of getting less than x occurrences.
-	:param x: Number of occurrences.
+    :param x: Number of occurrences.
-	:param l: Average number of occurrences.
+    :param l: Average number of occurrences.
-	:return: Returns the cumulative probability of getting from x occurrences.
+    :return: Returns the cumulative probability of getting less than x occurrences.
-	"""
+    """
-	return 1 - pd_upto(x - 1, l)
+    return sum(pd(i, l) for i in range(x))
+
+
+def pd_geq(x, l):
+    """
+    Computes the cumulative probability of getting from x occurrences.
+    :param x: Number of occurrences.
+    :param l: Average number of occurrences.
+    :return: Returns the cumulative probability of getting from x occurrences.
+    """
+    return 1 - pd_lt(x, l)
+
+
+def pd_gt(x, l):
+    """
+    Computes the cumulative probability of getting from x occurrences.
+    :param x: Number of occurrences.
+    :param l: Average number of occurrences.
+    :return: Returns the cumulative probability of getting from x occurrences.
+    """
+    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.
+    """
+
+    return cdf.normal_dist_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.
+    """
+    return cdf.normal_dist_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():
-	print("This module contains functions for computing the total probability of events.")
+    """
-	print("The functions are:")
+    Prints the manual for the module.
-	print("bnd(x, n, p) - The binomial distribution")
+    """
-	print("bnd_mean(n, p) - The mean of the binomial distribution")
+    separator = "-" * 20
-	print("bnd_var(n, p) - The variance of the binomial distribution")
+    print("This module contains functions for computing the total probability of events.")
-	print("bnd_std(n, p) - The standard deviation of the binomial distribution")
+    print("The functions are:")
-	print("bnd_upto(x, n, p) - The cumulative probability of getting upto x successes in n trials")
+    print(separator)
-	print("bnd_from(x, n, p) - The cumulative probability of getting from x successes in n trials")
+    print("Binomial Distribution")
-	print("gd(x, p, q) - The geometric distribution")
+    print("bnd(x, n, p)")
-	print("gd_mean(p) - The mean of the geometric distribution")
+    print("bnd_mean(n, p)")
-	print("gd_var(p) - The variance of the geometric distribution")
+    print("bnd_var(n, p)")
-	print("gd_std(p) - The standard deviation of the geometric distribution")
+    print("bnd_std(n, p)")
-	print("gd_upto(x, p) - The cumulative probability of getting upto x trials until the first success")
+    print("bnd_leq(x, n, p)")
-	print("gd_from(x, p) - The cumulative probability of getting from x trials until the first success")
+    print("bnd_lt(x, n, p)")
-	print("hgd(x, N, n, k) - The hyper geometric distribution")
+    print("bnd_geq(x, n, p)")
-	print("hgd_mean(N, n, k) - The mean of the hyper geometric distribution")
+    print("bnd_gt(x, n, p)")
-	print("hgd_var(N, n, k) - The variance of the hyper geometric distribution")
+    print(separator)
-	print("hgd_std(N, n, k) - The standard deviation of the hyper geometric distribution")
+    print("Geometric Distribution")
-	print(
+    print("gd(x, p, q)")
-		"hgd_upto(x, N, n, k) - The cumulative probability of getting upto x successes in n draws from a population of size N with k successes")
+    print("gd_mean(p)")
-	print(
+    print("gd_var(p)")
-		"hgd_from(x, N, n, k) - The cumulative probability of getting from x successes in n draws from a population of size N with k successes")
+    print("gd_std(p)")
-	print("pd(x, l) - The poisson distribution")
+    print("gd_leq(x, p, q)")
-	print("pd_mean(l) - The mean of the poisson distribution")
+    print("gd_lt(x, p, q)")
-	print("pd_var(l) - The variance of the poisson distribution")
+    print("gd_geq(x, p, q)")
-	print("pd_std(l) - The standard deviation of the poisson distribution")
+    print("gd_gt(x, p, q)")
-	print("pd_upto(x, l) - The cumulative probability of getting upto x occurrences")
+    print(separator)
-	print("pd_from(x, l) - The cumulative probability of getting from x occurrences")
+    print("Hyper Geometric Distribution")
+    print("hgd(x, N, n, k)")
+    print("hgd_mean(N, n, k)")
+    print("hgd_var(N, n, k)")
+    print("hgd_std(N, n, k)")
+    print("hgd_leq(x, N, n, k)")
+    print("hgd_lt(x, N, n, k)")
+    print("hgd_geq(x, N, n, k)")
+    print("hgd_gt(x, N, n, k)")
+    print(separator)
+    print("Poisson Distribution")
+    print("pd(x, l)")
+    print("pd_mean(l)")
+    print("pd_var(l)")
+    print("pd_std(l)")
+    print("pd_leq(x, l)")
+    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)")

law_total_probability.py

@@ -34,9 +34,12 @@ def n(A):
 
 
 def man():
+	"""
+	Prints the manual for the module.
+	"""
 	print("This module contains functions for computing the total probability of events.")
 	print("The functions are:")
-	print("i(A, B) - The intersection of A and B")
+	print("i(A, B)")
-	print("u(A, B) - The union of A and B")
+	print("u(A, B)")
-	print("g(A, B) - The conditional probability of A given B")
+	print("g(A, B)")
-	print("n(A) - The negation of A")
+	print("n(A)")

netcentric.py

@@ -0,0 +1,105 @@
+# Calculate internet checksum for any arbitrary length variable amount of binary numbers
+def checksum(*args):
+	length = len(bin(args[0])) - 2
+	result = 0
+	for arg in args:
+		result += arg
+		if result > (2 ** length) - 1:
+			result = (result & ((2 ** length) - 1)) + 1
+	return result ^ ((2 ** length) - 1)
+
+
+def e2e_delay(P, L, N, R):
+	# P = propagation speed
+	# L = packet length
+	# N = number of packets
+	# R = transmission rate
+	return (P - 1) * (L / R) + N * (L / R)
+
+
+def estimate_e2e_delay(PS, T):
+	# PS = packet size
+	# T = Throughput
+	return PS / T
+
+
+def trans_delay(L, R):
+	# L = packet length
+	# R = transmission rate
+	return L / R
+
+
+def prop_delay(P, L):
+	# P = propagation speed
+	# L = packet length
+	return P * L
+
+
+def traffic_intensity(L, pps, R):
+	# L = packet length
+	# pps = packets per second
+	# R = transmission rate
+	return (L * pps) / R
+
+
+def cs_time(N, F, U):
+	# N = Number of copies
+	# F = File size
+	# U = Server upload rate
+	return (N * F) / U
+
+
+def cs_time_n_clients(N, F, U, D):
+	# N = Number of copies
+	# F = File size
+	# U = Server upload rate
+	# D = Client download rate
+	return max(cs_time(N, F, U), F / D)
+
+
+def p2p_time(N, F, U, CD, D):
+	# N = Number of copies
+	# F = File size
+	# U = Server upload rate
+	# CU = Client upload rate
+	# D = Client download rate
+	return max((F / U), (N * F) / (U + (N * CD)), F / D)
+
+
+def utilisation(L, R, RTT):
+	# L = packet length
+	# R = transmission rate
+	# RTT = round trip time
+	return (L / R) / (L / R + RTT)
+
+
+def utilisation_pipeline(L, R, RTT, N):
+	# L = packet length
+	# R = transmission rate
+	# RTT = round trip time
+	# N = window size
+	return N / (1 + (RTT / (L / R)))
+
+
+def print_byte_tables():
+	print("Byte Conversion Table")
+	print("1 B = 8 bits")
+	print("kB = 1024 bytes")
+	print("MB = 1024 kB")
+	print("GB = 1024 MB")
+	print("TB = 1024 GB")
+
+
+def man():
+	print("checksum(0b, 0b,)")
+	print("e2e_delay(P, L, N, R)")
+	print("estimate_e2e_delay(PS, T)")
+	print("trans_delay(L, R)")
+	print("prop_delay(P, L)")
+	print("traffic_intensity(L, pps, R)")
+	print("cs_time(N, F, U)")
+	print("cs_time_n_clients(N, F, U, D)")
+	print("p2p_time(N, F, U, CD, D)")
+	print("utilisation(L, R, RTT)")
+	print("utilisation_pipeline(L, R, RTT, N)")
+	print("print_byte_tables()")