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 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 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 confidence_interval(data):
"""
Calculate confidence interval for mean
:param data: list of int or float values
:return: list with confidence interval
"""
if ch.check_list(data):
return [
avg.average(data) - (1.96 * SEM(data)),
avg.average(data) + (1.96 * SEM(data))
]
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 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 oscillation_coefficient(data):
"""
Calculate coefficient of oscillation
:param data: list of int or float values
:return: oscillation coefficient
"""
if ch.check_list(data):
R = base.range(data)
x = avg.average(data)
return R / x
def coefficient_of_variation(data):
"""
Calculate coefficient of variation
:param data: list of int or float values
:return: variation coefficient
"""
if ch.check_list(data):
b = vars.standard_deviation(data)
x = avg.average(data)
return b / x
def relative_linear_deviation(data):
"""
Calculate linear deviation coefficient
:param data: list of int or float values
:return: relative linear deviation coefficient
"""
if ch.check_list(data):
d = vars.mean_linear_deviation(data)
x = avg.average(data)
return d / x
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 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 sample_dispersion(data):
"""
Calculate sample dispersion
:param data: list of int or float values
:return: S^2
"""
if ch.check_list(data):
n = len(data)
d = 0
for element in data:
d += element**2
return (d / n) - (avg.average(data)**2)
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 mean_linear_deviation(data):
"""
Calculate simple linear deviation
:param data: list of int or float values
:return: linear deviation
"""
if ch.check_list(data):
mean = avg.average(data)
n = len(data)
d = 0
for element in data:
d += np.fabs(element - mean)
return d / n
def unbiased_variance_estimate(data):
"""
Calculate dispersion variance
:param data: list of int or float values
:return: dict with variance estimate and sqrt of dispersion variance
"""
if ch.check_list(data):
mean = avg.average(data)
n = len(data)
d = 0
for element in data:
d += (element - mean)**2
return {'S2': d / (n - 1), 's': np.sqrt(d / (n - 1))}
def dispersion(data):
"""
Calculate dispersion
:param data: list of int or float values
:return: (sigma^2)
"""
if ch.check_list(data):
mean = avg.average(data)
n = len(data)
d = 0
for element in data:
d += (element - mean)**2
return d / n