Source code for ineqpy.api

"""API's module.

Extend pandas.DataFrames with the main functions from statistics and
inequality modules.
"""
import inspect

from types import MethodType
from functools import partial

import pandas as pd

from . import inequality, statistics


[docs]class Convey: """Convey.""" def __init__( self, data=None, index=None, columns=None, weights=None, group=None, **kw ): self.df = pd.DataFrame(data=data, index=index, columns=columns, **kw) self.weights = weights self.group = group self._attach_method(statistics, self) self._attach_method(inequality, self) @property
[docs] def _constructor(self): return Survey
@classmethod
[docs] def _attach_method(module, instance): # get methods names contained in module res_names = list() res_methods = [] method_name_list = inspect.getmembers(module, inspect.isfunction) for method_name, func in method_name_list: # if method_name.startswith('_'): continue # avoid private methods func = getattr(module, method_name) # get function if ( "weights" in inspect.signature(func).parameters ): # replace weights variable func = partial(func, weights=instance.weights) # func = partial(func, data=instance.data) func = MethodType(func, instance) res_methods.append(func) res_names.append(method_name) setattr(instance, method_name, func)
[docs]class Survey: """Survey it's a data structure that handles survey data. Attributes ---------- df : pandas.DataFrame weights : str group : str Methods ------- atkinson(income=None, weights=None, e=0.5) Calculate Atkinson's index. avg_tax_rate(total_tax=None, total_base=None, weights=None) Calculate average tax rate. c_moment(variable=None, weights=None, order=2, param=None, ddof=0) Calculate central momment. coef_variation(variable=None, weights=None) Calculate coefficient of variation. concentration(income=None, weights=None, sort=True) Calculate concentration's index. density(variable=None, weights=None, groups=None) Calculate density. gini(income=None, weights=None, sort=True) Calculate Gini's index. kakwani(tax=None, income_pre_tax=None, weights=None) Calculate Kakwani's index. kurt(variable=None, weights=None) Calculate Kurtosis. lorenz(income=None, weights=None) Calculate Lorenz curve. mean(variable=None, weights=None) Calculate mean. percentile(variable=None, weights=None, p=50, interpolate="lower") Calculate percentile. reynolds_smolensky(income_pre_tax=None, income_post_tax=None, weights=None) Calculate Reynolds-Smolensky's index. skew(variable=None, weights=None) Calculate Skew. std_moment(variable=None, weights=None, param=None, order=3, ddof=0) Calculate standard deviation. theil(income=None, weights=None) Calculate Theil's index. var(variable=None, weights=None, ddof=0) Calculate variance. """ def __init__( self, data=None, index=None, columns=None, weights=None, group=None, **kw ): self.df = pd.DataFrame(data=data, index=index, columns=columns, **kw) self.weights = weights self.group = group
[docs] def c_moment(self, variable, weights=None, order=2, param=None, ddof=0): """Calculate central momment. Calculate the central moment of `x` with respect to `param` of order `n`, given the weights `w`. Parameters ---------- variable : 1d-array Variable weights : 1d-array Weights order : int, optional Moment order, 2 by default (variance) param : int or array, optional Parameter for which the moment is calculated, the default is None, implies use the mean. ddof : int, optional Degree of freedom, zero by default. Returns ------- central_moment : float Notes ----- - The cmoment of order 1 is 0 - The cmoment of order 2 is the variance. Source : https://en.wikipedia.org/wiki/Moment_(mathematics) Todo ---- Implement: https://en.wikipedia.org/wiki/L-moment#cite_note-wang:96-6 """ data = self.df if weights is None: weights = self.weights return statistics.c_moment(variable, weights, data, order, param, ddof)
[docs] def percentile(self, variable, weights=None, p=50, interpolate="lower"): """Calculate the value of a quantile given a variable and his weights. Parameters ---------- data : pd.DataFrame, optional pd.DataFrame that contains all variables needed. variable : str or array weights : str or array q : float Quantile level, if pass 0.5 means median. interpolate : bool Returns ------- percentile : float or pd.Series """ data = self.df if weights is None: weights = self.weights return statistics.percentile(variable, weights, data, p, interpolate)
[docs] def std_moment(self, variable, weights=None, param=None, order=3, ddof=0): """Calculate the standardized moment. Calculate the standardized moment of order `c` for the variable` x` with respect to `c`. Parameters ---------- data : pd.DataFrame, optional pd.DataFrame that contains all variables needed. variable : 1d-array Random Variable weights : 1d-array, optional Weights or probability order : int, optional Order of Moment, three by default param : int or float or array, optional Central trend, default is the mean. ddof : int, optional Degree of freedom. Returns ------- std_moment : float Returns the standardized `n` order moment. References ---------- - https://en.wikipedia.org/wiki/Moment_(mathematics)#Significance_ of_the_moments - https://en.wikipedia.org/wiki/Standardized_moment Todo ---- It is the general case of the raw and central moments. Review implementation. """ data = self.df if weights is None: weights = self.weights return statistics.std_moment( variable, weights, data, param, order, ddof )
[docs] def mean(self, variable, weights=None): """Calculate the mean of `variable` given `weights`. Parameters ---------- variable : array-like or str Variable on which the mean is estimated. weights : array-like or str Weights of the `x` variable. data : pandas.DataFrame Is possible pass a DataFrame with variable and weights, then you must pass as `variable` and `weights` the column name stored in `data`. Returns ------- mean : array-like or float """ # if pass a DataFrame separate variables. data = self.df if weights is None: weights = self.weights return statistics.mean(variable, weights, data)
[docs] def density(self, variable, weights=None, groups=None): """Calculate density in percentage. This make division of variable inferring width in groups as max - min. Parameters ---------- data : pd.DataFrame, optional pandas.DataFrame that contains all variables needed. variable : array-like, optional weights : array-like, optional groups : array-like, optional Returns ------- density : array-like References ---------- Histogram. (2017, May 9). In Wikipedia, The Free Encyclopedia. Retrieved: https://en.wikipedia.org/w/index.php?title=Histogram """ data = self.df if weights is None: weights = self.weights return statistics.density(variable, weights, groups, data)
[docs] def var(self, variable, weights=None, ddof=0): """Calculate the population variance of `variable` given `weights`. Parameters ---------- data : pd.DataFrame, optional pd.DataFrame that contains all variables needed. variable : 1d-array or pd.Series or pd.DataFrame Variable on which the quasivariation is estimated weights : 1d-array or pd.Series or pd.DataFrame Weights of the `variable`. Returns ------- variance : 1d-array or pd.Series or float Estimation of quasivariance of `variable` References ---------- Moment (mathematics). (2017, May 6). In Wikipedia, The Free Encyclopedia. Retrieved 14:40, May 15, 2017, from https://en.wikipedia.org/w/index.php?title=Moment_(mathematics) Notes ----- If stratificated sample must pass with groupby each strata. """ data = self.df if weights is None: weights = self.weights return statistics.var(variable, weights, data, ddof)
[docs] def coef_variation(self, variable, weights=None): """Calculate the coefficient of variation. The coefficient of variation is the square root of the variance of the incomes divided by the mean income. It has the advantages of being mathematically tractable and is subgroup decomposable, but is not bounded from above. Parameters ---------- data : pandas.DataFrame variable : array-like or str weights : array-like or str Returns ------- coefficient_variation : float References ---------- Coefficient of variation. (2017, May 5). In Wikipedia, The Free Encyclopedia. Retrieved 15:03, May 15, 2017, from https://en.wikipedia.org/w/index.php?title=Coefficient_of_variation """ # TODO complete docstring data = self.df if weights is None: weights = self.weights return statistics.coef_variation(variable, weights, data)
[docs] def kurt(self, variable, weights=None): """Calculate the asymmetry coefficient. Parameters ---------- variable : 1d-array w : 1d-array Returns ------- kurt : float Kurtosis coefficient. References ---------- Moment (mathematics). (2017, May 6). In Wikipedia, The Free Encyclopedia. Retrieved 14:40, May 15, 2017, from https://en.wikipedia.org/w/index.php?title=Moment_(mathematics) Notes ----- It is an alias of the standardized fourth-order moment. """ data = self.df if weights is None: weights = self.weights return statistics.kurt(variable, weights, data)
[docs] def skew(self, variable, weights=None): """Return the asymmetry coefficient of a sample. Parameters ---------- data : pandas.DataFrame variable : array-like, str weights : array-like, str Returns ------- skew : float References ---------- Moment (mathematics). (2017, May 6). In Wikipedia, The Free Encyclopedia. Retrieved 14:40, May 15, 2017, from https://en.wikipedia.org/w/index.php?title=Moment_(mathematics)& oldid=778996402 Notes ----- It is an alias of the standardized third-order moment. """ data = self.df if weights is None: weights = self.weights return statistics.skew(variable, weights, data)
# INEQUALITY #  ----------
[docs] def concentration(self, income, weights=None, sort=True): """Calculate concentration index. This function calculate the concentration index, according to the notation used in [Jenkins1988]_ you can calculate the: C_x = 2 / x · cov(x, F_x) if x = g(x) then C_x becomes C_y when there are taxes: y = g(x) = x - t(x) Parameters ---------- income : array-like weights : array-like data : pandas.DataFrame sort : bool Returns ------- concentration : array-like References ---------- Jenkins, S. (1988). Calculating income distribution indices from micro-data. National Tax Journal. http://doi.org/10.2307/41788716 """ # TODO complete docstring data = self.df if weights is None: weights = self.weights return inequality.concentration(income, weights, data, sort)
[docs] def lorenz(self, income, weights=None): """Calculate lorenz curve. In economics, the Lorenz curve is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for representing grouped of the wealth distribution. This function compute the lorenz curve and returns a DF with two columns of axis x and y. Parameters ---------- data : pandas.DataFrame A pandas.DataFrame that contains data. income : str or 1d-array, optional Population or wights, if a DataFrame is passed then `income` should be a name of the column of DataFrame, else can pass a pandas.Series or array. weights : str or 1d-array Income, monetary variable, if a DataFrame is passed then `y`is a name of the series on this DataFrame, however, you can pass a pd.Series or np.array. Returns ------- lorenz : pandas.Dataframe Lorenz distribution in a Dataframe with two columns, labeled x and y, that corresponds to plots axis. References ---------- Lorenz curve. (2017, February 11). In Wikipedia, The Free Encyclopedia. Retrieved 14:34, May 15, 2017, from https://en.wikipedia.org/w/index.php?title=Lorenz_curve&oldid=764853675 """ data = self.df if weights is None: weights = self.weights return inequality.lorenz(income, weights, data)
[docs] def gini(self, income, weights=None, sort=True): """Calculate Gini's index. The Gini coefficient (sometimes expressed as a Gini ratio or a normalized Gini index) is a measure of statistical dispersion intended to represent the income or wealth distribution of a nation's residents, and is the most commonly used measure of grouped. It was developed by Corrado Gini. The Gini coefficient measures the grouped among values of a frequency distribution (for example, levels of income). A Gini coefficient of zero expresses perfect equality, where all values are the same (for example, where everyone has the same income). A Gini coefficient of 1 (or 100%) expresses maximal grouped among values (e.g., for a large number of people, where only one person has all the income or consumption, and all others have none, the Gini coefficient will be very nearly one). Parameters ---------- data : pandas.DataFrame DataFrame that contains the data. income : str or np.array, optional Name of the monetary variable `x` in` df` weights : str or np.array, optional Name of the series containing the weights `x` in` df` sorted : bool, optional If the DataFrame is previously ordered by the variable `x`, it's must pass True, but False by default. Returns ------- gini : float Gini Index Value. Notes ----- The calculation is done following (discrete probability distribution): G = 1 - [∑_i^n f(y_i)·(S_{i-1} + S_i)] where: - y_i = Income - S_i = ∑_{j=1}^i y_i · f(y_i) Reference --------- - Gini coefficient. (2017, May 8). In Wikipedia, The Free Encyclopedia. Retrieved 14:30, May 15, 2017, from https://en.wikipedia.org/w/index.php?title=Gini_coefficient&oldid=779424616 - Jenkins, S. (1988). Calculating income distribution indices from micro-data. National Tax Journal. http://doi.org/10.2307/41788716 Todo ---- - Implement statistical deviation calculation, VAR (GINI) """ data = self.df if weights is None: weights = self.weights return inequality.gini(income, weights, data, sort)
[docs] def atkinson(self, income, weights=None, e=0.5): """Calculate Atkinson index. More precisely labelled a family of income grouped measures, the theoretical range of Atkinson values is 0 to 1, with 0 being a state of equal distribution. An intuitive interpretation of this index is possible: Atkinson values can be used to calculate the proportion of total income that would be required to achieve an equal level of social welfare as at present if incomes were perfectly distributed. For example, an Atkinson index value of 0.20 suggests that we could achieve the same level of social welfare with only 1 – 0.20 = 80% of income. The theoretical range of Atkinson values is 0 to 1, with 0 being a state of equal distribution. Parameters ---------- income : array or str If `data` is none `income` must be an 1D-array, when `data` is a pd.DataFrame, you must pass the name of income variable as string. weights : array or str, optional If `data` is none `weights` must be an 1D-array, when `data` is a pd.DataFrame, you must pass the name of weights variable as string. e : int, optional Epsilon parameter interpreted by atkinson index as grouped adversion, must be a number between 0 to 1. data : pd.DataFrame, optional data is a pd.DataFrame that contains the variables. Returns ------- atkinson : float Reference --------- Atkinson index. (2017, March 12). In Wikipedia, The Free Encyclopedia. Retrieved 14:35, May 15, 2017, from https://en.wikipedia.org/w/index.php?title=Atkinson_index&oldid=769991852 Todo ---- - Implement: CALCULATING INCOME DISTRIBUTION INDICES FROM MICRO-DATA http://www.jstor.org/stable/41788716 - The results has difference with stata, maybe have a bug. """ data = self.df if weights is None: weights = self.weights return inequality.atkinson(income, weights, data, e)
[docs] def kakwani(self, tax, income_pre_tax, weights=None): """Calculate kakwani's index. The Kakwani (1977) index of tax progressivity is defined as twice the area between the concentration curves for taxes and pre-tax income, or equivalently, the concentration index for t(x) minus the Gini index for x, i.e. K = C(t) - G(x) = (2/t) cov [t(x), F(x)] - (2/x) cov [x, F(x)]. Parameters ---------- data : pandas.DataFrame This variable is a DataFrame that contains all data required in columns. tax_variable : array-like or str This variable represent tax payment of person, if pass array-like then data must be None, else you pass str-name column in `data`. income_pre_tax : array-like or str This variable represent income of person, if pass array-like then data must be None, else you pass str-name column in `data`. weights : array-like or str This variable represent weights of each person, if pass array-like then data must be None, else you pass str-name column in `data`. Returns ------- kakwani : float References ---------- Jenkins, S. (1988). Calculating income distribution indices from micro-data. National Tax Journal. http://doi.org/10.2307/41788716 """ # main calc data = self.df if weights is None: weights = self.weights return inequality.kakwani(tax, income_pre_tax, weights, data)
[docs] def reynolds_smolensky( self, income_pre_tax, income_post_tax, weights=None ): """Calculate Reynolds-Smolensky's index. The Reynolds-Smolensky (1977) index of the redistributive effect of taxes, which can also be interpreted as an index of progressivity (Lambert 1985), is defined as: L = Gx - Gy = [2/x]cov[x,F(x)] - [2/ybar] cov [y, F(y)]. Parameters ---------- data : pandas.DataFrame This variable is a DataFrame that contains all data required in it's columns. income_pre_tax : array-like or str This variable represent tax payment of person, if pass array-like then data must be None, else you pass str-name column in `data`. income_post_tax : array-like or str This variable represent income of person, if pass array-like then data must be None, else you pass str-name column in `data`. weights : array-like or str This variable represent weights of each person, if pass array-like then data must be None, else you pass str-name column in `data`. Returns ------- reynolds_smolensky : float References ---------- Jenkins, S. (1988). Calculating income distribution indices from micro-data. National Tax Journal. http://doi.org/10.2307/41788716 """ data = self.df if weights is None: weights = self.weights return inequality.reynolds_smolensky( income_pre_tax, income_post_tax, weights, data )
[docs] def theil(self, income, weights=None): """Calculate theil index. The Theil index is a statistic primarily used to measure economic grouped and other economic phenomena. It is a special case of the generalized entropy index. It can be viewed as a measure of redundancy, lack of diversity, isolation, segregation, grouped, non-randomness, and compressibility. It was proposed by econometrician Henri Theil. Parameters ---------- data : pandas.DataFrame This variable is a DataFrame that contains all data required in it's columns. income : array-like or str This variable represent tax payment of person, if pass array-like then data must be None, else you pass str-name column in `data`. weights : array-like or str This variable represent weights of each person, if pass array-like then data must be None, else you pass str-name column in `data`. Returns ------- theil : float References ---------- Theil index. (2016, December 17). In Wikipedia, The Free Encyclopedia. Retrieved 14:17, May 15, 2017, from https://en.wikipedia.org/w/index.php?title=Theil_index&oldid=755407818 """ data = self.df if weights is None: weights = self.weights return inequality.theil(income, weights, data)
[docs] def avg_tax_rate(self, total_tax, total_base, weights=None): """Compute the average tax rate given a base income and a total tax. Parameters ---------- total_base : str or numpy.array total_tax : str or numpy.array data : pd.DataFrame Returns ------- avg_tax_rate : float or pd.Series Is the ratio between mean the tax income and base of income. Reference --------- Panel de declarantes de IRPF 1999-2007: Metodología, estructura y variables. (2011). Panel de declarantes de IRPF 1999-2007: Metodología, estructura y variables. Documentos. """ data = self.df if weights is None: weights = self.weights return inequality.avg_tax_rate(total_tax, total_base, weights, data)
[docs] def top_rest( self, income, weights=None, data=None, top_percentage=10 ): """Calculate the 10:90 Ratio. Calculates the quotient between the number of contributions from the top 10% of contributors divided by the number contributions made by the other 90%. The ratio is 1 if the total contributions by the top contributors are equal to the cotnributions made by the rest; less than zero if the top 10% contributes less than the rest; and greater that 1 if the top 10% contributes more than the other ninety percent. Parameters ---------- income : array-like or str This variable represent tax payment of person, if pass array-like then data must be None, else you pass str-name column in `data`. weights : array-like or str This variable represent weights of each person, if pass array-like then data must be None, else you pass str-name column in `data`. All-ones by default data : pandas.DataFrame This variable is a DataFrame that contains all data required in it's columns. top_percentage : float The richest x percent to consider. (10 percent by default) It must be a number between 0 and 100 Returns ------- ratio : float References ---------- Participation Inequality in Wikis: A Temporal Analysis Using WikiChron. Serrano, Abel & Arroyo, Javier & Hassan, Samer. (2018). DOI: 10.1145/3233391.3233536. """ data = self.df if weights is None: weights = self.weights return inequality.top_rest(income, weights, data, top_percentage)