kern.fun {Ake} R Documentation

## 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")


[Package Ake version 1.0.1 Index]
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