API Module¶

Module contents¶

Poverty and Inequality Analysis.

Apode contains a set of measures applied in economics.

class apode.ApodeData(data, income_column)[source]¶

Bases: object

Poverty and Inequality Analysis in Python.

Apode is a package that contains a set of indicators that are applied in economic analysis. It contains measures of: - poverty - inequality - welfare - polarization - concentration

Parameters

data (dataframe) – Dataset to be analiced.
income_column (str) – Column name

data, income_column

apode.basic module¶

ApodeData class for Apode.

class apode.basic.ApodeData(data, income_column)[source]¶

Bases: object

Poverty and Inequality Analysis in Python.

Apode is a package that contains a set of indicators that are applied in economic analysis. It contains measures of: - poverty - inequality - welfare - polarization - concentration

Parameters

data (dataframe) – Dataset to be analiced.
income_column (str) – Column name

data, income_column

apode.concentration module¶

Concentration measures for Apode.

class apode.concentration.ConcentrationMeasures(idf)[source]¶

Bases: object

Concentration Measures.

The following concentration measures are implemented:

herfindahl : Herfindahl-Hirschman Index
rosenbluth : Rosenbluth Index
concentration_ratio : Concentration Ratio Index

Parameters

method (String) – Concentration measure.
**kwargs – Arbitrary keyword arguments.

concentration_ratio(k)[source]¶

Concentration Ratio index.

The concentration ratio is calculated as the sum of the market share percentage held by the largest specified number of firms in an industry.

Parameters: k (int) – The number of firms included in the concentration ratio calculation.
Returns: out – Index measure.
Return type: float

herfindahl(normalized=True)[source]¶

Herfindahl-Hirschman index.

The Herfindahl-Hirschman index it is defined as the sum of the squares of the market shares of the firms within the industry 1.

Parameters: normalized (bool(default=true)) – The normalized index ranges from 0 to 1.
Returns: out – Index measure.
Return type: float

References

1: Hirschman, A.O (1964), “The Paternity of an Index”, American Economic Review, 54 (5), 761.

rosenbluth()[source]¶

Rosenbluth index.

The Rosenbluth index measures the proportion of the population that counted as poor 2.

Returns: out – Index measure.
Return type: float

References

2: Rosenbluth, G. (1955). Measures of concentration, Business Concentration and Price Policy. National Bureau of Economic Research. Special Conference Series No. 5. Princeton, 57–89.

apode.datasets module¶

Data simulation tools for Apode.

apode.datasets.binning(df, pos=0, nbin=None)[source]¶

Binning function.

Agrupa valores de un dataframe en nbin categorías.

Parameters

df (DataFrame) –
pos (int, optional(default=0)) – Options are r: relative, ‘g’: generalized, ‘a’: absolut.
nbin (int, optional(default=None)) –

Returns

out – Grouped data

Return type

DataFrame

apode.datasets.make_bimodal(size=100, nbin=None)[source]¶

Bimodal Distribution.

Parameters

size (int, optional(default=100)) –
nbin (int, optional(default=None)) –

Returns

out

Return type

float array

apode.datasets.make_chisquare(seed=None, size=100, df=5, c=10, nbin=None)[source]¶

Chisquare Distribution.

Parameters

seed (int, optional(default=None)) –
size (int, optional(default=100)) –
df (float, optional(default=5)) –
c (float, optional(default=10)) –
nbin (int, optional(default=None)) –

Returns

out – Array of random numbers.

Return type

float array

apode.datasets.make_constant(size=100, nbin=None)[source]¶

Constant value Distribution.

Parameters

size (int, optional(default=100)) –
nbin (int, optional(default=None)) –

Returns

out

Return type

float array

apode.datasets.make_exponential(seed=None, size=100, scale=1, c=50, nbin=None)[source]¶

Exponential Distribution.

Parameters

seed (int, optional(default=None)) –
size (int, optional(default=100)) –
scale (float, optional(default=1.0)) –
c (float, optional(default=50)) –
nbin (int, optional(default=None)) –

Returns

out – Array of random numbers.

Return type

float array

apode.datasets.make_extreme(size=100, nbin=None)[source]¶

Extreme value Distribution.

Parameters

size (int, optional(default=100)) –
nbin (int, optional(default=None)) –

Returns

out

Return type

float array

apode.datasets.make_gamma(seed=None, size=100, shape=1, scale=50.0, nbin=None)[source]¶

Gamma Distribution.

Parameters

seed (int, optional(default=None)) –
size (int, optional(default=100)) –
shape (float, optional(default=1.0)) –
scale (float, optional(default=50.0)) –
nbin (int, optional(default=None)) –

Returns

out – Array of random numbers.

Return type

float array

apode.datasets.make_linear(size=100, nbin=None)[source]¶

Linear value Distribution.

Parameters

size (int, optional(default=100)) –
nbin (int, optional(default=None)) –

Returns

out

Return type

float array

apode.datasets.make_lognormal(seed=None, size=100, sigma=1.0, nbin=None)[source]¶

Lognormal Distribution.

Parameters

seed (int, optional(default=None)) –
size (int, optional(default=100)) –
sigma (float, optional(default=1.0)) –
nbin (int, optional(default=None)) –

Returns

out – Array of random numbers.

Return type

float array

apode.datasets.make_pareto(seed=None, a=5, size=100, c=200, nbin=None)[source]¶

Pareto Distribution.

Parameters

seed (int, optional(default=None)) –
a (float, optional(default=5)) –
size (int, optional(default=100)) –
c (int, optional(default=200)) –
nbin (int, optional(default=None)) –

Returns

out – Array of random numbers.

Return type

float array

apode.datasets.make_squared(size=100, nbin=None)[source]¶

Squared value Distribution.

Parameters

size (int, optional(default=100)) –
nbin (int, optional(default=None)) –

Returns

out

Return type

float array

apode.datasets.make_uniform(seed=None, size=100, mu=100, nbin=None)[source]¶

Uniform Distribution.

Parameters

seed (int, optional(default=None)) –
size (int, optional(default=100)) –
mu (float, optional(default=100)) –
nbin (int, optional(default=None)) –

Returns

out – Array of random numbers.

Return type

float array

apode.datasets.make_unimodal(size=100, nbin=None)[source]¶

Unimodal Distribution.

Parameters

size (int, optional(default=100)) –
nbin (int, optional(default=None)) –

Returns

out

Return type

float array

apode.datasets.make_weibull(seed=None, size=100, a=1.5, c=50, nbin=None)[source]¶

Weibull Distribution.

Parameters

seed (int, optional(default=None)) –
size (int, optional(default=100)) –
a (float, optional(default=1.5)) –
c (float, optional(default=50)) –
nbin (int, optional(default=None)) –

Returns

out – Array of random numbers.

Return type

float array

apode.inequality module¶

Inequality measures for Apode.

class apode.inequality.InequalityMeasures(idf)[source]¶

Bases: object

Inequality measures for Apode.

The following inequality measures are implemented:

gini: Gini Index
entropy: Generalized Entropy Index
atkinson: Atkinson Index
rrange: Relative Range
rad: Relative average deviation
cv: Coefficient of variation
sdlog: Standard deviation of log
merhan: Merhan index
piesch: Piesch Index
bonferroni: Bonferroni Indices
kolm: Kolm Index

Parameters

method (String) – Inequality measure.
**kwargs – Arbitrary keyword arguments.

atkinson(alpha=2)[source]¶

Atkinson index.

The Atkinson index measures the proportion of the population that counted as poor. 12

Parameters: alpha (float, optional(default=2)) –
Returns: out – Index measure.
Return type: float

References

12: Atkinson, AB (1970) On the measurement of inequality. Journal of Economic Theory, 2 (3), pp. 244–263.

bonferroni()[source]¶

Bonferroni Coefficient.

The Bonferroni Coefficient 10.

Returns: out – Index measure.
Return type: float

References

10: Bonferroni, C.E. (1930), Elementi di Statistica Generale, Seeber, Firenze.

cv()[source]¶

Coefficient of variation.

It is the quotient between the standard deviation and the mean. 4

Returns: out – Index measure.
Return type: float

References

4: Atkinson, AB (1970) On the measurement of inequality. Journal of Economic Theory, 2 (3), pp. 244–263.

entropy(alpha=0)[source]¶

General Entropy index.

The entropy index measures the proportion of the population that counted as poor.

Parameters: alpha (float, optional(default=0)) –
Returns: out – Index measure.
Return type: float

gini()[source]¶

Gini Coefficient.

The Gini Coefficient 7.

Returns: out – Index measure.
Return type: float

References

7: Gini, C. (1914), ‘Sulla misura della concentrazione e della variabilità dei caratteri’, Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti 73, 1203-1248.

kolm(alpha)[source]¶

Kolm Coefficient.

The Kolm Coefficient 11

Parameters: alpha (float) –
Returns: out – Index measure.
Return type: float

References

11: Kolm, S.-Ch. (1 976a). ‘Unequal Inequalitites 1’, Journal of Economic Theory.

merhan()[source]¶

Merhan Coefficient.

The Merhan Coefficient 8.

Returns: out – Merhan Coefficient.
Return type: float

References

8: Mehran, Farhad, 1976. “Linear Measures of Income Inequality,” Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.

piesch()[source]¶

Piesch Coefficient.

The Piesch Coefficient 9.

Returns: out – Index measure.
Return type: float

References

9: Piesch, W. (1975). Statistische Konzentrationsmasse. Mohr (Paul Siebeck), Tübingen.

rad()[source]¶

Relative average deviation.

Ratio of the sum of the absolute value of the distance between each income in the distribution and the mean income, to total income. 3

Returns: out – Index measure.
Return type: float

References

3: Atkinson, AB (1970) On the measurement of inequality. Journal of Economic Theory, 2 (3), pp. 244–263.

ratio(alpha)[source]¶

Dispersion Ratio (Kuznets Ratio).

This measure presents the ratio of the average income of the richest alpha percent of the population to the average income of the poorest alpha percent 6.

Parameters: alpha (float) –
Returns: out – Index measure.
Return type: float

References

6: Haughton, J., and Khandker, S. R. (2009). Handbook on poverty and inequality. Washington, DC: World Bank.

rrange()[source]¶

Relative range.

This measure divides the difference between the highest and lowest income by the mean income.

Returns: out – Index measure.
Return type: float

sdlog()[source]¶

Calculate Standard deviation of logarithms.

Attach great importance to income transfers at the lower end. 5

Returns: out – Index measure.
Return type: float

References

5: Atkinson, AB (1970) On the measurement of inequality. Journal of Economic Theory, 2 (3), pp. 244–263.

apode.plots module¶

Plots for Apode.

class apode.plots.PlotAccessor(idf)[source]¶

Bases: object

Plots for Apode.

The following plots are implemented:

hist : Histogram (default)
lorenz : Lorenz curve (relative, generalized, absolute)
pen : Pen Parade
tip : Tip curve

Parameters

method (String) – Plot type.
**kwargs – Arbitrary keyword arguments.

lorenz(alpha='r', ax=None, **kwargs)[source]¶

Lorenz Curve.

A Lorenz curve is a graphical representation of the distribution of income or wealth within a population. Lorenz curves graph percentiles of the population against cumulative income or wealth of people at or below that percentile. 13

Parameters

alpha (string, optional(default='r')) – Options are r: relative, ‘g’: generalized, ‘a’: absolut.
ax (axes object, optional) –

Returns

out – Matplotlib plot

Return type

plot

References

13: Lorenz, M. O. (1905). Methods for measuring concentration of wealth. Journal of the American Statistical Association 9, 209-219.

pen(pline=None, ax=None, **kwargs)[source]¶

Pen Parade Curve.

Pen’s Parade or The Income Parade is a concept described in a 1971 book published by Dutch economist Jan Pen describing income distribution. The parade is defined as a succession of every person in the economy, with their height proportional to their income, and ordered from lowest to greatest. 14

Parameters

pline (float, optional) –
ax (axes object, optional) –

Returns

out – Matplotlib plot

Return type

plot

References

14: Pen, J. (1971). Income Distribution. London: Allen Lane, The Penguin Press.

tip(pline, ax=None, **kwargs)[source]¶

TIP Curve.

Three ‘I’s of Poverty (TIP) curves, based on distributions of poverty gaps, provide evocative graphical summaries of the incidence, intensity, and inequality dimensions of poverty, and a means for checking for unanimous poverty orderings according to a wide class of poverty indices. 15

Parameters

pline (float, optional) –
ax (axes object, optional) –

Returns

out – Matplotlib plot

Return type

plot

References

15: Jenkins S. P., Lambert P., 1997. Three “I’s of Poverty” Curves, with an Analysis of UK Poverty Trends, Oxford Economic Papers, 49, pp. 317-327.

apode.polarization module¶

Polarization measures for Apode.

class apode.polarization.PolarizationMeasures(idf)[source]¶

Bases: object

Polarization Measures.

The following welfare measures are implemented:

ray : Esteban and Ray index
wolfson : Wolfson index

Parameters: method (String) – Polarization measure.

ray()[source]¶

Esteban and Ray index of polarization.

Esteban and Ray index of polarization. 16

Returns: out – Polarization measure.
Return type: float

References

16: Esteban, J.M. y D. Ray (1994), “On the Measurement of Polarization”, Econometrica, vol. 62, N. 4, julio, pp. 819-851.

wolfson()[source]¶

Wolfson index of bipolarization.

Wolfson index of bipolarization (normalized). 17

Returns: out – Polarization measure.
Return type: float

References

17: Wolfson, Michael C. 1994. “When Inequalities Diverge.” The American Economic Review 84 (2): 353–58.

apode.poverty module¶

Poverty measures for Apode.

class apode.poverty.PovertyMeasures(idf)[source]¶

Bases: object

Poverty Measures.

The following poverty measures are implemented:

headcount: Headcount Index
gap: Poverty gap Index
severity: Poverty Severity Index
fgt: Foster–Greer–Thorbecke Indices
sen: Sen Index
sst: Sen-Shorrocks-Thon Index
watts: Watts Index
cuh: Clark, Ulph and Hemming Indices
takayama: Takayama Index
kakwani: Kakwani Indices
thon: Thon Index
bd: Blackorby and Donaldson Indices
hagenaars: Hagenaars Index
chakravarty: Chakravarty Indices

Parameters

method (String) – Poverty measure.
**kwargs – Arbitrary keyword arguments.

bd(pline=None, alpha=2, factor=1.0, q=None)[source]¶

Blackorby and Donaldson Indices.

Blackorby y Donaldson (1980) proponen una medida de pobreza de tipo normativo. 29

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’
alpha (float, optional(default=2)) – Aversion parameter. (ver)

Returns

out – Index measure in [0,1].

Return type

float

References

29: Blackorby, C. y Donaldson, D. (1980). “Ethical indices for the measurement of poverty”. Econometrica. Vol. 48, n 4, pp.1053–1060.

chakravarty(pline=None, alpha=0.5, factor=1.0, q=None)[source]¶

Chakravarty Indices.

Chakravarty (1983) es una medida ética de pobreza. El índice de pobreza se obtiene como la suma normalizada de las carencias de utilidad de los pobres. 31

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’
alpha (float, optional(default=0.5)) – Aversion parameter. (ver)

Returns

out – Index measures.

Return type

float

References

31: Chakravarty, S.R. (1983). “A new index of poverty”. Mathematical Social Sciences. Vol. 6, pp.307–313.

cuh(pline=None, alpha=0.5, factor=1.0, q=None)[source]¶

Clark, Ulph and Hemming index.

Clark, Hemming y Ulph (1981) proponen utilizar en la medida de pobreza de Sen, la medida de Atkinson en lugar del índice de Gini de los pobres. 25

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’
alpha (float, optional(default=0.5)) – Atkinson parameter.

Returns

out – Index measure in [0,1].

Return type

float

References

25: Clark, S.R.; Hemming, R. y Ulph, D. (1981). “On indices for the measurement of poverty”. Economic Journal. Vol. 91, pp.515–526.

fgt(pline=None, alpha=0, factor=1.0, q=None)[source]¶

Foster–Greer–Thorbecke Indices.

When parameter α = 0, P0 is simply the headcount index. When α = 1, the index is the poverty gap index P1, and when α is set equal to 2, P2 is the poverty severity index. A α se le conoce con el nombre de parámetro de aversión a la pobreza y, por tanto, cuanto mayor sea α, más énfasis se le da al más pobre de los pobres. 21

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’
alpha (float, optional(default=0)) – Aversion poverty parameter.

Returns

out – Index measure in [0, 1].

Return type

float

References

21: Foster, J.E.; Greer, J. y Thorbecke, E. (1984). “A class of decomposable poverty measures”. Econometrica. Vol. 52, n 3, pp.761–766.

gap(pline=None, factor=1.0, q=None)[source]¶

Poverty gap index.

The poverty gap index adds up the extent to which individuals on average fall below the poverty line, and expresses it as a percentage of the poverty line. 19

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’

Returns

out – Index measure [0, 1].

Return type

float

References

19: Haughton, J., and Khandker, S. R. (2009). Handbook on poverty and inequality. Washington, DC: World Bank.

hagenaars(pline=None, factor=1.0, q=None)[source]¶

Hagenaars Index.

Hagenaars (1984) para obtener la medida de pobreza considera la función de evaluación social de la renta como V(x) = ln(x). 30

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’

Returns

out – Index measure [unbounded].

Return type

float

References

30: Hagenaars, A. (1984). “A class of poverty indices”. Center for Research in Public Economics. Leyden University.

headcount(pline=None, factor=1.0, q=None)[source]¶

Headcount index.

The headcount index measures the proportion of the population that counted as poor. 18

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’

Returns

out – Index measure.

Return type

float

References

18: Haughton, J., and Khandker, S. R. (2009). Handbook on poverty and inequality. Washington, DC: World Bank.

kakwani(pline=None, alpha=2, factor=1.0, q=None)[source]¶

Kakwani Indices.

La familia de Kakwani (1980) que pondera los déficit mediante una potencia del número de orden que ocupa cada individuo dentro del subgrupo de pobres. El parámetro α identifica una cierta “aversión” al lugar ocupado en la sociedad. 27

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’
alpha (float, optional(default=2)) – Aversion parameter.

Returns

out – Index measure in [0, 1].

Return type

float

References

27: Kakwani, Nanak (1980). “On a Class of Poverty Measures”. Econometrica, vol.48, n.2, pp.437-446

sen(pline=None, factor=1.0, q=None)[source]¶

Sen Index.

Sen (1976) proposed an index that seeks to combine the effects of the number of poor, the depth of their poverty, and the distribution poverty within the group. 22

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’

Returns

out – Index measure in [0, 1].

Return type

float

References

22: Sen, A. (1976). “Poverty: an ordinal approach to measurement”. Econometrica 44(2), pp.219–231.

severity(pline=None, factor=1.0, q=None)[source]¶

Squared Poverty Gap (Poverty Severity) Index.

To construct a measure of poverty that takes into account inequality among the poor, some researchers use the squared poverty gap index. This is simply a weighted sum of poverty gaps (as a proportion of the poverty line), where the weights are the proportionate poverty gaps themselves. 20

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’

Returns

out – Index measure in [0, 1].

Return type

float

References

20: Haughton, J., and Khandker, S. R. (2009). Handbook on poverty and inequality. Washington, DC: World Bank.

sst(pline=None, factor=1.0, q=None)[source]¶

Sen-Shorrocks-Thon Index Index.

The Sen index has been modified by others, and one of the most attractive versions is the Sen-Shorrocks-Thon (SST) index. One strength of the SST index is that it can help give a good sense of the sources of change in poverty over time. This is because the index can be decomposed. 23

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’

Returns

out – Index measure.

Return type

float

References

23: Xu, K. (1998). Statistical inference for the Sen-Shorrocks-Thon index of poverty intensity. Journal of Income Distribution, 8, 143-152.

takayama(pline=None, factor=1.0, q=None)[source]¶

Takayama Index.

Takayama (1979) define su medida de pobreza calculando el índice de Gini de la distribución censurada por la línea de pobreza. 26

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’

Returns

out – Index measure in [0,1].

Return type

float

References

26: Takayama, N. (1979). “Poverty, income inequality, and their measures: Professor Sen’s axiomatic approach reconsidered”. Econometrica. Vol. 47, n 3, pp.747–759.

thon(pline=None, factor=1.0, q=None)[source]¶

Thon Index.

La diferencia entre esta medida (Thon,1979) y la de Sen radica en la función de ponderación. Aquí se pondera el individuo pobre por el lugar que ocupa dentro de toda la población, y no solo respecto a los pobres. 28

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’

Returns

out – Index measure.

Return type

float

References

28: Thon, D. (1979). “On measuring poverty”. Review of Income and Wealth. Vol. 25, pp.429–439.

watts(pline=None, factor=1.0, q=None)[source]¶

Watts index.

Harold Watts (1968) propuso la siguiente medida de pobreza sensible a la distribución de rentas. 24

Parameters

pline (optional(default=None)) – Absolute poverty line if pline is float. Relative poverty line if pline is ‘median’, ‘quantile’ or ‘mean’ If pline is None then pline = 0.5*median(y).
factor (float, optional(default=1.0)) – Factor in pline = factor*stat
q (float, optional(default=None)) – Cuantil q if pline is’quantile’

Returns

out – Index measure [0,inf].

Return type

float

References

24: Watts, H. (1968). “An economic definition of poverty”, en D. P. Moynihan. On Understanding Poverty. Basic Books. Inc. New York, pp.316–329.

apode.welfare module¶

Welfare measures for Apode.

class apode.welfare.WelfareMeasures(idf)[source]¶

Bases: object

Welfare Measures.

The following welfare measures are implemented:

utilitarian : Utilitarian utility function
rawlsian : Rawlsian utility function
isoelastic : Isoelastic utility function
sen : Sen utility function
theill : Theill utility function
theilt : Theilt utility function

Parameters

method (String) – Welfare measure.
**kwargs – Arbitrary keyword arguments.

isoelastic(alpha)[source]¶

Isoelastic utility function.

The isoelastic utility function.

Returns: out – Utility value.
Return type: float

rawlsian()[source]¶

Rawlsian utility function.

The rawlsian utility function.

Returns: out – Utility value.
Return type: float

sen()[source]¶

Sen utility function.

The Sen utility function.

Returns: out – Utility value.
Return type: float

theill()[source]¶

Theil L utility function.

The Theil L utility function.

Returns: out – Utility value.
Return type: float

theilt()[source]¶

Theil T utility function.

The Theil T utility function.

Returns: out – Utility value.
Return type: float

utilitarian()[source]¶

Utilitarian utility function.

The utilitarian utility function.

Returns: out – Utility value.
Return type: float