moment_functionals: Moments, central moments, mean, variance, standard deviation,...

In JonasMoss/polygrams: Density Estimation with Mixtures of Disjoint Bernstein Polynomials

Description

Moments, central moments, mean, variance, standard deviation, skewness and (excess) kurtosis for Bernstein polygrams.

Usage

mean_polygram(polygram_object)

moment_polygram(polygram_object, moment = 1)

central_moment_polygram(polygram_object, moment = 2)

var_polygram(polygram_object)

sd_polygram(polygram_object)

skewness_polygram(polygram_object)

kurtosis_polygram(polygram_object, excess = FALSE)

Arguments

polygram_object	a polygram object.
moment	positive integer, specifying which moment to calculate.
excess	logical, only for kurtosis; if TRUE (default), the excess kurtosis is calculated.

Details

A Bernstein polygram on [a, b] is disjoint mixture of rescaled Bernstein densities on subintervals of [a, b]. Such polygrams can be used for non-parametric density estimation, as an alternative to logsplines and kernel density estimation. These functions help with calculating moments.

Value

mean returns the expected value, var the variance, sd the standard deviation, moment the pth moment, central_moment the pth central moment, skewness the skewness, and kurtosis the kurtosis.

Functions

• mean_polygram: Calculates the mean of a Bernstein polygram.

• moment_polygram: Calculates the pth moment of a Bernstein polygram.

• central_moment_polygram: Calculates the pth central moment of a Bernstein polygram.

• var_polygram: Calculates the variance of a Bernstein polygram.

• sd_polygram: Calculates the standard deviation of a Bernstein polygram.

• skewness_polygram: Calculates the skewness of a Bernstein polygram.

• kurtosis_polygram: Calculates the (excess) kurtosis of a Bernstein polygram.

Examples

## Do a parametric bootstrap.
set.seed(1337)
data = rbeta(200, 2, 7)
polygram_object = polygram(data, s = 3, m = 4)
current_median = qpolygram(0.5, polygram_object)
medians = replicate(100, {
  new_data = rpolygram(200, polygram_object)
  new_median = qpolygram(0.5, polygram(new_data, s = 3, m = 4))
  new_median
})
plot(polygram(sqrt(200)*(current_median - medians), s = 4, m = 4,
              support = c(-1,1)))

JonasMoss/polygrams documentation built on Nov. 8, 2019, 5:19 p.m.