def factorial(n):
"""
:return: returns the factorial of a number
"""
if ch.check_number(n):
i = 1
fact = 1
while i <= n:
fact *= i
i += 1
return fact
def moment(data, degree):
"""
Calculate central moments
:param data: list of int or float values
:return: value of central moment
"""
if ch.check_list(data) and ch.check_number(degree):
mean = avg.average(data)
M = 0
for element in data:
M += (element - mean)**degree
return M / len(data)
def fisher_criteria(x, y, m):
"""
Value of fisher criteria
:param x: list of dependent variable
:param y: list of independent variable
:param m: the number of influencing factors in the trend model
:return: value of fisher criteria
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y) and ch.check_number(m):
numerator = determination_coefficient(x, y) * (len(x) - m - 1)
denumerator = (1 - determination_coefficient(x, y)) * m
return numerator / denumerator
def dispersion_error_equation(x, y, m):
"""
Dispersion error equations
:param x: list of dependent variable
:param y: list of independent variable
:param m: the number of influencing factors in the trend model
:return: value of dispersion error
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y) and ch.check_number(m):
numerator = 0
yxl = yx(x, y)
for yi, yxl in zip(y, yxl):
numerator += (yi - yxl)**2
return numerator / (len(y) - m - 1)
def accomodations_with_repeats(n, k):
"""
:return: value of accomodations with repeats
"""
if ch.check_number(n) and ch.check_number(k):
return n**k
def combinations_with_repeats(n, m):
"""
:return: value of combinations with repeats
"""
if ch.check_number(n) and ch.check_number(m):
return factorial(n + m - 1) / (factorial(n - 1) * factorial(m))
def accommodations(n, k):
"""
:return: the number of allocations of n elements in k
"""
if ch.check_number(n) and ch.check_number(k):
return factorial(n) / factorial(n - k)
def combinations(n, m):
"""
:return: number of combinations of n by m
"""
if ch.check_number(n) and ch.check_number(m):
return factorial(n) / (factorial(m) * factorial(n - m))