ineqpy.statistics

Descriptive statistics.

This module contains main descriptive statistics like: mean, variance, etc.

Module Contents

Functions

c_moment([variable, weights, data, order, param, ddof])	Calculate central momment.
percentile([variable, weights, data, p, interpolate])	Calculate the value of a quantile given a variable and his weights.
std_moment([variable, weights, data, param, order, ddof])	Calculate standarized momment.
mean([variable, weights, data])	Calculate the mean of variable given weights.
density([variable, weights, groups, data])	Density in percentage.
var([variable, weights, data, ddof])	Calculate the variance.
coef_variation([variable, weights, data])	Calculate the coefficient of variation.
kurt([variable, weights, data])	Calculate the Kurtosis coefficient.
skew([variable, weights, data])	Return the asymmetry coefficient of a sample.

ineqpy.statistics.c_moment(variable=None, weights=None, data=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:

variable1d-array

Variable

weights1d-array

Weights

datapandas.DataFrame

Contains all variables needed.

orderint, optional

Moment order, 2 by default (variance)

paramint or array, optional

Parameter for which the moment is calculated, the default is None, implies use the mean.

ddofint, optional

Degree of freedom, zero by default.

Returns:

central_momentfloat

Notes

• The cmoment of order 1 is 0

• The cmoment of order 2 is the variance.

Source : https://en.wikipedia.org/wiki/Moment_(mathematics)

ineqpy.statistics.percentile(variable=None, weights=None, data=None, p=50, interpolate='lower')

Calculate the value of a quantile given a variable and his weights.

Parameters:

variablestr or array

weightsstr or array

datapd.DataFrame, optional

pd.DataFrame that contains all variables needed.

qfloat

Quantile level, if pass 0.5 means median.

interpolatebool

Returns:

percentilefloat or pd.Series

ineqpy.statistics.std_moment(variable=None, weights=None, data=None, param=None, order=3, ddof=0)

Calculate standarized momment.

Calculate the standardized moment of order c for the variable` x` with respect to c.

Parameters:

variable1d-array

Random Variable

weights1d-array, optional

Weights or probability

datapd.DataFrame, optional

pd.DataFrame that contains all variables needed.

orderint, optional

Order of Moment, three by default

paramint or float or array, optional

Central trend, default is the mean.

ddofint, optional

Degree of freedom.

Returns:

std_momentfloat

Returns the standardized n order moment.

References

• https://en.wikipedia.org/wiki/Moment_(mathematics)

• https://en.wikipedia.org/wiki/Standardized_moment

ineqpy.statistics.mean(variable=None, weights=None, data=None)

Calculate the mean of variable given weights.

Parameters:

variablearray-like or str

Variable on which the mean is estimated.

weightsarray-like or str

Weights of the x variable.

datapandas.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:

meanarray-like or float

ineqpy.statistics.density(variable=None, weights=None, groups=None, data=None)

Density in percentage.

Calculates density in percentage. This make division of variable inferring width in groups as max - min.

Parameters:

variablenumpy.array or pandas.DataFrame

Main variable.

weightsnumpy.array or pandas.DataFrame

Weights of main variable.

groupsnumpy.array or pandas.DataFrame

Label that show which group each element belongs to.

datapd.DataFrame, optional

Object that contains all variables needed.

Returns:

densityarray-like

References

Histogram. (2017, May 9). In Wikipedia, The Free Encyclopedia. Retrieved 14:47, May 15, 2017, from https://en.wikipedia.org/w/index.php?title=Histogram&oldid=779516918

ineqpy.statistics.var(variable=None, weights=None, data=None, ddof=0)

Calculate the variance.

Calculate the population variance of variable given weights.

Parameters:

datapd.DataFrame, optional

pd.DataFrame that contains all variables needed.

variable1d-array or pd.Series or pd.DataFrame

Variable on which the quasivariation is estimated

weights1d-array or pd.Series or pd.DataFrame

Weights of the variable.

datapd.DataFrame

Object that contains all variables needed.

ddofint

Degree of freedom.

Returns:

variance1d-array or pd.Series or float

Estimation of quasivariance of variable

Notes

If stratificated sample must pass with groupby each strata.

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)

ineqpy.statistics.coef_variation(variable=None, weights=None, data=None)

Calculate the coefficient of variation.

Calculate the coefficient of variation of a variable given weights. 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:

variablearray-like or str

weightsarray-like or str

datapandas.DataFrame

Returns:

coefficient_variationfloat

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

ineqpy.statistics.kurt(variable=None, weights=None, data=None)

Calculate the Kurtosis coefficient.

Parameters:

variable1d-array

weights1d-array

datapandas.DataFrame

Object which stores variable and weights.

Returns:

kurtfloat

Kurtosis coefficient.

Notes

It is an alias of the standardized fourth-order moment.

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)

ineqpy.statistics.skew(variable=None, weights=None, data=None)

Return the asymmetry coefficient of a sample.

Parameters:

datapandas.DataFrame

variablearray-like, str

weightsarray-like, str

datapandas.DataFrame

Object which stores variable and weights.

Returns:

skewfloat

Notes

It is an alias of the standardized third-order moment.

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)