pycvcqv 0.7.0

Coefficient of Variation (CV) and Coefficient of Quartile Variation (CQV) with Confidence Intervals (CI)

pycvcqv

Find homogeneity with confidence.

Python port of cvcqv

Introduction

pycvcqv provides versatile functions to quantify homogeneity with confidence intervals. It offers a variety of well-established methods from the literature (Kelley, McKay, Miller, Vangel, Mahmoudvand-Hassani, Equal-Tailed, Shortest-Length, Normal Approximation, Bonett, and the Abu-Shawiesh-Akyuz-Kibria adjusted-degrees-of-freedom, large-sample, and augmented-large-sample CIs) and bootstrap resampling techniques (Normal, Basic, Percentile, BCa) for constructing confidence intervals on the Coefficient of Variation (cv) and the Coefficient of Quartile Variation (cqv).

Coefficient of Variation

cv is a measure of relative dispersion representing the degree of variability relative to the mean (Albatineh et al., 2014). Since cv is unitless, it is useful for comparing variables that have different units. It is also a measure of homogeneity (Albatineh et al., 2014).

Coefficient of Quartile Variation

cqv is a measure of relative dispersion based on the interquartile range (IQR). Since cqv is unitless, it is also useful for comparing variables that have different units. It is also a measure of homogeneity (Bonett, 2006; Altunkaynak, 2018).

Install

pip install pycvcqv

Usage

import pandas as pd
from pycvcqv import coefficient_of_variation, cqv

coefficient_of_variation(
    data=[
        0.2, 0.5, 1.1, 1.4, 1.8, 2.3, 2.5, 2.7, 3.5, 4.4,
        4.6, 5.4, 5.4, 5.7, 5.8, 5.9, 6.0, 6.6, 7.1, 7.9
    ],
    multiplier=100,
    ndigits=2
)
# {'cv': 57.77, 'lower': 41.43, 'upper': 98.38}
cqv(
    data=[0.2, 0.5, 1.1, 1.4, 1.8, 2.3, 2.5, 2.7, 3.5, 4.4, 4.6, 5.4, 5.4],
    multiplier=100,
)
# 51.7241
data = pd.DataFrame(
    {
        "col-1": pd.Series([0.2, 0.5, 1.1, 1.4, 1.8, 2.3, 2.5, 2.7, 3.5]),
        "col-2": pd.Series([5.4, 5.4, 5.7, 5.8, 5.9, 6.0, 6.6, 7.1, 7.9]),
    }
)
coefficient_of_variation(data=data, num_threads=3)
#   columns      cv      lower      upper
# 0   col-1  0.6076     0.3770     1.6667
# 1   col-2  0.1359     0.0913     0.2651
cqv(data=data, num_threads=-1)
#   columns      cqv
# 0   col-1  0.3889
# 1   col-2  0.0732

Confidence-interval methods for cv

coefficient_of_variation accepts a method argument that selects the confidence-interval estimator.

from pycvcqv import coefficient_of_variation

x = [
    0.2, 0.5, 1.1, 1.4, 1.8, 2.3, 2.5, 2.7, 3.5, 4.4,
    4.6, 5.4, 5.4, 5.7, 5.8, 5.9, 6.0, 6.6, 7.1, 7.9,
]

for method in (
    "kelley", "mckay", "miller", "vangel",
    "mahmoudvand_hassani", "equal_tailed",
    "shortest_length", "normal_approximation",
    "aak_adj", "aak_ls", "aak_als",
    "norm", "basic", "perc", "bca",
):
    print(method, coefficient_of_variation(
        data=x,
        method=method,
        multiplier=100,
        ndigits=3,
        num_replicates=10000,
        random_state=42,
    ))

Output (95% CI, multiplier=100, ndigits=3, bootstrap methods use num_replicates=10000, random_state=42):

method	est	lower	upper	description
kelley	57.774	41.303	97.950	cv with Kelley 95% CI
mckay	57.774	41.441	108.483	cv with McKay 95% CI
miller	57.774	34.053	81.495	cv with Miller 95% CI
vangel	57.774	40.955	103.931	cv with Vangel 95% CI
mahmoudvand_hassani	57.774	43.476	82.857	cv with Mahmoudvand-Hassani 95% CI
equal_tailed	57.774	43.937	84.383	cv with Equal-Tailed 95% CI
shortest_length	57.774	42.015	81.013	cv with Shortest-Length 95% CI
normal_approximation	57.774	44.533	85.272	cv with Normal Approximation 95% CI
aak_adj	57.774	48.029	72.516	cv with Abu-Shawiesh-Akyuz-Kibria Adjusted-DoF 95% CI
aak_ls	57.774	46.310	72.075	cv with Abu-Shawiesh-Akyuz-Kibria Large-Sample 95% CI
aak_als	57.774	45.839	75.092	cv with Abu-Shawiesh-Akyuz-Kibria Augmented-LS 95% CI
norm	57.774	38.850	78.379	cv with Normal Approximation Bootstrap 95% CI
basic	57.774	37.716	77.166	cv with Basic Bootstrap 95% CI
perc	57.774	38.382	77.832	cv with Bootstrap Percentile 95% CI
bca	57.774	41.556	83.032	cv with Adjusted Bootstrap Percentile (BCa) 95% CI

Confidence-interval methods for cqv

cqv accepts a method argument that selects the confidence-interval estimator. When method is omitted only the point estimate is returned (the legacy behavior).

from pycvcqv import cqv

x = [
    0.2, 0.5, 1.1, 1.4, 1.8, 2.3, 2.5, 2.7, 3.5, 4.4,
    4.6, 5.4, 5.4, 5.7, 5.8, 5.9, 6.0, 6.6, 7.1, 7.9,
]

for method in ("bonett", "norm", "basic", "perc", "bca"):
    print(method, cqv(
        data=x,
        method=method,
        multiplier=100,
        ndigits=3,
        num_replicates=10000,
        random_state=42,
    ))

Output (95% CI, multiplier=100, ndigits=3, bootstrap methods use num_replicates=10000, random_state=42):

method	est	lower	upper	description
bonett	45.625	24.785	77.329	cqv with Bonett 95% CI
norm	45.625	19.937	70.403	cqv with Normal Approximation Bootstrap 95% CI
basic	45.625	21.081	73.923	cqv with Basic Bootstrap 95% CI
perc	45.625	17.327	70.169	cqv with Bootstrap Percentile 95% CI
bca	45.625	22.006	76.331	cqv with Adjusted Bootstrap Percentile (BCa) 95% CI

Credits

This project was generated with python-package-template