kern.fun {Ake}

The associated kernel function

Description

The (S3) generic function kern.fun computes the value of the associated kernel function. Its default method does so with a given kernel and bandwidth h.

Usage

kern.fun(x, ...)
## Default S3 method:
kern.fun(x, t, h, type_data = c("discrete", "continuous"),
 ker = c("bino", "triang", "dirDU", "BE", "GA", "LN", "RIG"), 
a0 = 0, a1 = 1, a = 1, c = 2, ...)

Arguments

x

The target

t

A single value or the grid where the discrete associated kernel function is computed.

h

The bandwidth or smoothing parameter.

type_data

The sample data type

ker

The associated kernel: "dirDU" DiracDU,"bino" Binomial, "triang" Discrete Triangular kernel, "BE" extended beta, "GA" gamma, "LN" lognormal and "RIG" reciprocal inverse Gaussian.

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 0 for beta kernel.

a

The arm in Discrete Triangular kernel. The default value is 1.

c

The number of categories in DiracDU kernel. The default value is 2.

...

Further arguments

Details

The associated kernel is one of the those which have been defined in the sections above : extended beta, gamma,lognormal, reciprocal inverse Gaussian, DiracDU, Binomial and Discrete Triangular; see Kokonendji and Senga Kiessé (2011), and also Kokonendji et al. (2007).

Value

Returns the value of the discrete associated kernel function at t according to the target and the bandwidth.

Author(s)

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

References

Kokonendji, C.C. and Senga Kiessé, T. (2011). Discrete associated kernel method and extensions, Statistical Methodology 8, 497 - 516.

Kokonendji, C.C., Senga Kiessé, T. and Zocchi, S.S. (2007). Discrete triangular distributions and non-parametric estimation for probability mass function, Journal of Nonparametric Statistics 19, 241 - 254.

Examples

x<-5
h<-0.2
t<-0:10
kern.fun(x,t,h,"discrete","bino")