asymmetry.measures0.2 package

Asymmetry Measures for Probability Density Functions

d.sample

Switch between a range of probability density functions.

edf

Empirical cummulative distribution function

Epanechnikov

Epanechnikov kernel

eta.s.exact

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

eta.s

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

eta.w.breve.bc

Asymmetry coefficient η˘\breve{\eta} using boundary correction

eta.w.breve

Asymmetry coefficient η˘\breve{\eta}

eta.w.hat.bc

Asymmetry coefficient η^\hat{\eta} using boundary correction

eta.w.hat

Asymmetry coefficient η^\hat{\eta}

eta.w.tilde.bc

Asymmetry coefficient η~\tilde{\eta} using boundary correction

eta.w.tilde

Asymmetry coefficient η~\tilde{\eta}

IntEpanechnikov

Integrated Epanechnikov function

IntKde

Integrated Kernel density estimator

kde

Kernel density estimator.

p.sample

Switch between a range of available cumulative distribution functions.

pdfsq

Calculate f2(x)f^2(x)

pdfsqcdf

Calculate f2(x)F(x)f^2(x)F(x)

pdfsqcdfstar

Calculate f2(x)(1F(x))f^2(x)(1-F(x)).

pdfthird

Calculate f3(x)f^3(x)

q.sample

Switch between a range of available quantile functions.

r.sample

Switch between a range of available random number generators.

Rho.p.exact

Calculates the exact value ρp\rho_p, used in the implementation of the...

Rho.p

Calculates ρp\rho_p, used in the implementation of the strong asymmetr...

Rhostar.p.exact

Calculates the exact value of ρp\rho_p^*, used in the implementation o...

Rhostar.p

Calculates ρp\rho_p^*, used in the implementation of the strong asymme...

SimpsonInt

Simpson integration

Provides functions and examples for the weak and strong density asymmetry measures in the articles: "A measure of asymmetry", Patil, Patil and Bagkavos (2012) <doi:10.1007/s00362-011-0401-6> and "A measure of asymmetry based on a new necessary and sufficient condition for symmetry", Patil, Bagkavos and Wood (2014) <doi:10.1007/s13171-013-0034-z>. 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.

  • Maintainer: Dimitrios Bagkavos
  • License: GPL (>= 2)
  • Last published: 2020-07-22