dke.fun {Ake}

Function for density estimation

Description

The (S3) generic function dkde.fun computes the density. Its default method does so with the given kernel and bandwidth h.

Usage

dke.fun(Vec, ...)
## Default S3 method:
dke.fun(Vec, h, type_data = c("discrete", "continuous"), 
ker = c("BE", "GA", "LN", "RIG"), x = NULL, a0 = 0, a1 = 1, ... )

Arguments

Vec

The data sample from which the estimate is to be computed.

h

The bandwidth or smoothing parameter.

type_data

The data sample type. Data can be continuous or discrete (categorical or count). Here, in this function , we deal with continuous data.

ker

A character string giving the smoothing kernel to be used which is the associated kernel: "BE" extended beta, "GA" gamma, "LN" lognormal and "RIG" reciprocal inverse Gaussian.

x

The points of the grid at which the density is to be estimated.

a0

The left bound of the support used for extended beta kernel. Default value is 0 for beta kernel.

a1

The right bound of the support used for extended beta kernel. Default value is 1 for beta kernel.

...

Further arguments.

Details

The associated kernel estimator \widehat{f}_n of f is defined in the above sections. We recall that in general, the sum of the estimated values on the support is not equal to 1. In practice, we compute the global normalizing constant C_n before computing the estimated density \tilde{f}_n; see e.g. Libengué (2013).

Value

Returns a list containing:

data

The data - same as input Vec.

n

The sample size.

kernel

The asssociated kernel used to compute the density estimate.

h

The bandwidth used to compute the density estimate.

eval.points

The coordinates of the points where the density is estimated.

est.fn

The estimated density values.

C_n

The global normalizing constant.

hist

The histogram corresponding to the observations.

Author(s)

W. E. Wansouwé, S. M. Somé and C. C. Kokonendji

References

Libengué, F.G. (2013). Méthode Non-Paramétrique par Noyaux Associés Mixtes et Applications, Ph.D. Thesis Manuscript (in French) to Université de Franche-Comté, Besançon, France and Université de Ouagadougou, Burkina Faso, June 2013, LMB no. 14334, Besançon.

Examples

## A sample data with n=100.
V<-rgamma(100,1.5,2.6)
##The bandwidth can be the one obtained by cross validation.
h<-0.052
## We choose Gamma kernel.

est<-dke.fun(V,h,"continuous","GA")