def fehner_coefficient(x, y):
"""
Value of fehner coefficient
:param x: list of dependent variable
:param y: list of independent variable
:return: value of fehner coefficient
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
xa = avg.average(x)
ya = avg.average(y)
xlist = []
ylist = []
resulter = []
for xi in x:
if xi <= xa:
xlist.append("-")
else:
xlist.append("+")
for yi in y:
if yi <= ya:
ylist.append("-")
else:
ylist.append("+")
for xi, yi in zip(xlist, ylist):
if xi == yi:
resulter.append("A")
else:
resulter.append("B")
return (resulter.count("A") - resulter.count("B")) / (
resulter.count("A") + resulter.count("B"))
def durbin_watson(x, y):
"""
Find value for Durbin-Watrson criteria
:param x: list of dependent variable
:param y: list of independent variable
:return: value of Durbin-Watrson criteria
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
yx_list = yx(x, y)
e = []
for yi, yxi in zip(y, yx_list):
e.append(yi - yxi)
i = 0
e_ei = []
e_2 = []
for ei in e:
e_2.append(ei**2)
if i == 0:
i += 1
continue
else:
e_ei.append((e[i] - e[i - 1])**2)
i += 1
return sum(e_ei) / sum(e_2)
def covariation(x, y):
"""Find covariation coefficient
:param x: list of dependent variable
:param y: list of independent variable
:return: value of covariation coefficient
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
return avg.sample_average(x, y) - (avg.average(x) * avg.average(y))
def sost(x, y):
"""
Find value remains
:param x: list of dependent variable
:param y: list of independent variable
:return: value of remains
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
return total_amount(x, y) - sf(x, y)
def determination_coefficient(x, y):
"""
Finds determination coefficient
:param x: list of dependent variable
:param y: list of independent variable
:return: value of determination coefficient
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
return beta_coefficient(x, y)**2
def beta_coefficient(x, y):
"""
Finds beta coefficient
:param x: list of dependent variable
:param y: list of independent variable
:return: value of beta coefficient
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
return regression.pair_regression(x, y)['b'] * (
vars.sample_deviation(x) / vars.sample_deviation(y))
def sost_dispersion(x, y, p=2):
"""
Find value of ost dispersion
:param x: list of dependent variable
:param y: list of independent variable
:param p: number of factors
:return: value of ost dispersion
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
return sost(x, y) / (p * (len(x) - 1))
def elastic_coefficient(x, y):
"""
Finds elastic coefficient
:param x: list of dependent variable
:param y: list of independent variable
:return: value of elastic coefficient
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
return regression.pair_regression(
x, y)['b'] * (avg.average(x) / avg.average(y))
def closure_coefficient(x, y):
"""Find closure indicator
:param x: list of dependent variable
:param y: list of independent variable
:return: value of closure indicator
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
numerator = avg.sample_average(
x, y) - (avg.average(x) * avg.average(y))
denumerator = vars.sample_deviation(x) * vars.sample_deviation(y)
return numerator / denumerator
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 approximation_error(x, y):
"""Find approximation error
:param x: list of dependent variable
:param y: list of independent variable
:return: value in percent of approximation error
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
yxl = yx(x, y)
a = 0
for yi, yxli in zip(y, yxl):
a += (np.fabs(yi - yxli)) / yi
return 100 * (a / len(y))
def sample_average(x, y):
"""
Calculate sample average
:param x: list of int or float values
:param y: list of int or float values
:return: sample average
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
res = 0
n = len(x)
for xelem, yelem in zip(x, y):
res += xelem * yelem
return res / n
def sf(x, y, p=2):
"""
Find value sum for factor dispersion
:param x: list of dependent variable
:param y: list of independent variable
:param p: number of factors
:return: value of sum for factor dispersion
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
xavg = avg.average(x)
yavg = avg.average(y)
xyavg = (xavg + yavg) / 2
return len(x) * (xavg**2 + yavg**2 - p * (xyavg**2))
def expected_value(x, p):
"""
Find expected value of 2 datasets
:param x: list of int or float values
:param p: list of float values
:return: value of expected value
"""
if ch.check_list(x) and ch.check_list(p):
if ch.check_equality(x, p):
if ch.check_probability(p):
m = 0
for xi, pi in zip(x, p):
m += xi * pi
return m
def yx(x, y):
"""Auxiliary function for approximation error
:param x: list of dependent variable
:param y: list of independent variable
:return: list of regression values
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
yxl = []
a = pair_regression(x, y)['a']
b = pair_regression(x, y)['b']
for xi in x:
yxl.append(b * xi + a)
return yxl
def significance(x, y):
"""
Finds significance of correlation coefficient
:param x: list of dependent variable
:param y: list of independent variable
:return: value of significance of correlation coefficient
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
b = beta_coefficient(x, y)
n = len(x)
numerator = b * np.sqrt(n - 2)
denumerator = np.sqrt(1 - b * b)
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 tail_coefficient(x, y):
"""
Find tail mismatch coefficient
:param x: list of dependent variable
:param y: list of independent variable
:return: value of tail mismatch coefficient
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
numerator = 0
denumerator = 0
yxl = regression.yx(x, y)
for yi, yxl in zip(y, yxl):
numerator += (yi - yxl)**2
denumerator += yxl**2
return numerator / denumerator
def total_amount(x, y, p=2):
"""
Find value total amount
:param x: list of dependent variable
:param y: list of independent variable
:param p: number of factors
:return: value of total amount
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
x2 = []
y2 = []
xavg = avg.average(x)
yavg = avg.average(y)
xyavg = (xavg + yavg) / 2
for xi, yi in zip(x, y):
x2.append(xi * xi)
y2.append(yi * yi)
return sum(x2) + sum(y2) - len(x) * p * (xyavg * xyavg)
def pearson_correltaion(x, y):
"""Finds the Pearson correlation coefficient.
:param x: list of dependent variable
:param y: list of independent variable
:return: value with value of correlation coefficient
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
avg_x = avg.average(x)
avg_y = avg.average(y)
diffprod = 0
xdiff2 = 0
ydiff2 = 0
for idx in range(len(x)):
xdiff = x[idx] - avg_x
ydiff = y[idx] - avg_y
diffprod += xdiff * ydiff
xdiff2 += xdiff * xdiff
ydiff2 += ydiff * ydiff
return diffprod / np.sqrt(xdiff2 * ydiff2)
def pair_regression(x, y):
"""Find pair regression equation
:param x: list of dependent variable
:param y: list of independent variable
:return: dictionary with coefficients of regression
"""
if ch.check_list(x) and ch.check_list(y):
if ch.check_equality(x, y):
x2 = 0
for elem in x:
x2 += elem * elem
xy = 0
for xelem, yelem in zip(x, y):
xy += xelem * yelem
a = np.array([[len(x), sum(x)], [sum(x), x2]])
b = np.array([sum(y), xy])
system = np.linalg.solve(a, b)
result = system.tolist()
return {'a': result[0], 'b': result[1]}