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asymmetry.measures (version 0.2)

Asymmetry Measures for Probability Density Functions

Description

Provides functions and examples for the weak and strong density asymmetry measures in the articles: "A measure of asymmetry", Patil, Patil and Bagkavos (2012) and "A measure of asymmetry based on a new necessary and sufficient condition for symmetry", Patil, Bagkavos and Wood (2014) . The measures provided here are useful for quantifying the asymmetry of the shape of a density of a random variable. The package facilitates implementation of the measures which are applicable in a variety of fields including e.g. probability theory, statistics and economics.

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Version

Install

install.packages('asymmetry.measures')

Monthly Downloads

214

Version

0.2

License

GPL (>= 2)

Maintainer

Dimitrios Bagkavos

Last Published

July 22nd, 2020

Functions in asymmetry.measures (0.2)

Rhostar.p

Calculates \(\rho_p^*\), used in the implementation of the strong asymmetry measure \(\eta(X)\).
Rho.p

Calculates \(\rho_p\), used in the implementation of the strong asymmetry measure \(\eta(X)\).
GDP.Per.head.dist.1995

annual Gross Domestic Product (GDP) per head across 15 European Union (EU) countries
Rho.p.exact

Calculates the exact value \(\rho_p\), used in the implementation of the strong asymmetry measure \(\eta(X)\).
Epanechnikov

Epanechnikov kernel
GDP.Per.head.dist.2005

annual Gross Domestic Product (GDP) per head across 15 European Union (EU) countries
SimpsonInt

Simpson integration
eta.w.tilde.bc

Asymmetry coefficient \(\tilde{\eta}\) using boundary correction
eta.w.tilde

Asymmetry coefficient \(\tilde{\eta}\)
IntEpanechnikov

Integrated Epanechnikov function
eta.w.hat

Asymmetry coefficient \(\hat{\eta}\)
r.sample

Switch between a range of available random number generators.
q.sample

Switch between a range of available quantile functions.
p.sample

Switch between a range of available cumulative distribution functions.
kde

Kernel density estimator.
pdfsq

Calculate \(f^2(x)\)
eta.w.breve.bc

Asymmetry coefficient \(\breve{\eta}\) using boundary correction
eta.w.breve

Asymmetry coefficient \(\breve{\eta}\)
pdfsqcdf

Calculate \(f^2(x)F(x)\)
d.sample

Switch between a range of probability density functions.
edf

Empirical cummulative distribution function
eta.s

Strong asymmetry measure \(eta(X)\).
eta.s.exact

Strong asymmetry measure \(eta(X)\).
pdfsqcdfstar

Calculate \(f^2(x)(1-F(x))\).
eta.w.hat.bc

Asymmetry coefficient \(\hat{\eta}\) using boundary correction
pdfthird

Calculate \(f^3(x)\)
Rhostar.p.exact

Calculates the exact value of \(\rho_p^*\), used in the implementation of the strong asymmetry measure \(\eta(X)\).
IntKde

Integrated Kernel density estimator