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Author: SamiTumarov

maths/binomial_distribution.py

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+"""For more information about the Binomial Distribution -
+    https://en.wikipedia.org/wiki/Binomial_distribution"""
+
+
+def binomial_distribution(k, n, p) -> float:
+    """
+
+    Returns probability of k successes out of n tries,
+    with p probability for one success
+
+    use: binomial_distribution(k, n, p):
+    k - successes
+    n - independent Bernoulli trials
+    p - probability for one succes
+
+    The function uses the factorial function
+    in order to calculate the binomial coefficient
+
+    >>> binomial_distribution(3, 5, 0.7)
+    0.30870000000000003
+
+    >>> binomial_distribution (2, 4, 0.5)
+    0.375
+
+    >>> binomial_distribution (2, 4, -0.5)
+    Traceback (most recent call last):
+    ...
+    raise ValueError("p - Probability has to be in range of 1 - 0")
+    ValueError: p - Probability has to be in range of 1 - 0
+    """
+    if k > n:
+        raise ValueError("""k must be lower or equal to n""")
+    if n < 0 or k < 0 or type(k) != int or type(n) != int:
+        raise ValueError("the function is defined for non-negative integers k and n")
+    if p > 1 or p < 0:
+        raise ValueError("p - Probability has to be in range of 1 - 0")
+    probability = (p**k)*(1-p)**(n-k)
+    # Calculate the binomial coefficient:
+    # Calculate n! / k!(n-k)!
+    coefficient = factorial(n)/(factorial(k)*factorial(n-k))
+
+    return probability * coefficient
+
+
+# Implementation of the factorial function,
+# used to calculate the binomial coefficient:
+def factorial(n) -> int:
+    """
+    Factorial - The product of all positive integers less than or equal to n
+    """
+
+    if type(n) != int:
+        raise ValueError("factorial(n) accepts only integer values")
+    if n < 0:
+        raise ValueError("factorial(n) works only for non-negative numbers")
+    if n == 0:
+        return 1
+    result = 1
+    for i in range(1, n+1):
+        result *= i
+    return result
+
+if __name__ == "__main__":
+    print ("Probability of 2 successes out of 4 trails")
+    print ("with probability of 0.75 is : ")
+    print (str(binomial_distribution(2, 4, 0.75)))