Vitale: Class '"Vitale"'
In bde: Bounded Density Estimation

Vitale

R Documentation

Class `"Vitale"`

Description

This class deals with Vitale (1975) Bernstein Polynomial approximation as described in Leblanc (2009). The polynomial estimator is computed using the provided data samples. Using this polynomial estimator, the methods implemented in the class can be used to compute densities, values of the distribution function, quantiles, sample the distribution and obtain graphical representations.

Objects from the Class

Objects can be created by using the generator function vitale.

Slots

dataPointsCache:: a numeric vector containing points within the [lower.limit,upper.limit] interval
densityCache:: a numeric vector containing the density for each point in dataPointsCache
distributionCache:: a numeric vector used to cache the values of the distribution function. This slot is included to improve the performance of the methods when multiple calculations of the distribution function are used
dataPoints:: a numeric vector containing data samples within the [lower.limit,upper.limit] interval. These data samples are used to obtain the kernel estimator
m:: the order of the polynomial approximation
lower.limit:: a numeric value for the lower limit of the bounded interval for the data
upper.limit:: a numeric value for the upper limit of the bounded interval for the data

Methods

density: See "density" for details
distribution: See "distribution" for details
quantile: See "quantile" for details
rsample: See "rsample" for details
plot: See "plot" for details
getdataPointsCache: See "getdataPointsCache" for details
getdensityCache: See "getdensityCache" for details
getdistributionCache: See "getdistributionCache" for details
getdataPoints: See "getdataPoints" for details
getm: See "getm" for details

Author(s)

Guzman Santafe, Borja Calvo and Aritz Perez

References

Vitale, R. A. (1975). A Bernstein polynomial approach to density function estimation. Statistical Inference and Related Topics, 2, 87-99.

Leblanc, A. (2010). A bias-reduced approach to density estimation using Bernstein polynomials. Journal of Nonparametric Statistics, 22(4), 459-475.

Examples

# create the model 
model <- vitale(dataPoints = tuna.r, m = 25)


# examples of usual functions
density(model,0.5)

distribution(model,0.5,discreteApproximation=FALSE)
 
# graphical representation
hist(tuna.r,freq=FALSE,main="Tuna Data")
lines(model, col="red",lwd=2)

# graphical representation using ggplot2 
graph <- gplot(model, show=TRUE, includePoints=TRUE)

bde documentation built on June 10, 2022, 5:10 p.m.