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")
```

*Ake*version 1.0.1 Index]