kef {Ake} | R Documentation |

## Continuous and discrete associated kernel function

### Description

This function computes the associated kernel function.

### Usage

```
kef(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 associated kernel function is computed. |

`h` |
The bandwidth or smoothing parameter. |

`type_data` |
The sample data type |

`ker` |
The associated kernel:"bino" Binomial, "triang" discrete triangular kernel, "BE" extended beta, "GA" gamma, "LN" lognormal and "RIG" reciprocal inverse Gaussian,"dirDU" DiracDU. |

`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. |

`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. |

### 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 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

Chen, S. X. (1999). Beta kernels estimators for density functions, *Computational Statistics and Data Analysis* **31**, 131 - 145.

Chen, S. X. (2000). Probability density function estimation using gamma kernels, *Annals of the Institute of Statistical Mathematics* **52**, 471 - 480.

Igarashi, G. and Kakizawa, Y. (2015). Bias correction for some asymmetric kernel estimators, *Journal of Statistical Planning and Inference* **159**, 37 - 63.

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.

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

```
x<-5
h<-0.2
t<-0:10
kef(x,t,h,"discrete","bino")
```

*Ake*version 1.0.1 Index]