| Title: | Estimating Count Data Distributions with Discrete Optimal Symmetric Kernel |
| Version: | 1.0.0 |
| Maintainer: | Thomas Fillon <thomas.fillon@univ-ubs.fr> |
| Description: | Implementation of Discrete Symmetric Optimal Kernel for estimating count data distributions, as described by T. Senga Kiessé and G. Durrieu (2024) <doi:10.1016/j.spl.2024.110078>.The nonparametric estimator using the discrete symmetric optimal kernel was illustrated on simulated data sets and a real-word data set included in the package, in comparison with two other discrete symmetric kernels. |
| License: | GPL (≥ 3) |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Imports: | stats |
| Suggests: | knitr, rmarkdown, testthat (≥ 3.0.0) |
| Config/testthat/edition: | 3 |
| VignetteBuilder: | knitr |
| Depends: | R (≥ 2.10) |
| LazyData: | true |
| URL: | https://thomasfillon.github.io/kernopt/, https://github.com/thomasfillon/kernopt |
| BugReports: | https://github.com/thomasfillon/kernopt/issues |
| NeedsCompilation: | no |
| Packaged: | 2025-03-18 14:11:14 UTC; rstudio |
| Author: | Tristan Senga Kiesse
 [aut],
Gilles Durrieu
[aut],
Thomas Fillon
[aut, cre],
INRAE, Institut Agro, CNRS - UMR SAS [cph],
Université de Bretagne Sud, CNRS - UMR 6205 LMBA [cph] |
| Repository: | CRAN |
| Date/Publication: | 2025-03-19 13:20:05 UTC |
Cross-Validation function for bandwidth parameter selection of discrete kernel
Description
Cross-Validation function for bandwidth parameter selection of discrete kernel
Usage
cv_bandwidth(
kernel = c("optimal", "triang", "epanech", "binomial"),
v,
h,
k = NULL
)
Arguments
kernel |
the type of kernel. Currently supported kernels are limited to: "optimal", "triang", "epanech" and "binomial" |
v |
the vector of observations |
h |
the list of bandwidth parameters to test in cross validation |
k |
Optional: the integer (positive) parameter that defined the support of the kernel function (corresponds to parameter 'a' for triangular kernel). It is only used for optimal and triangular kernel |
Value
the optimal bandwidth value
Examples
n <- 250
mu <- 2 # Mean
y <- sort(rpois(n, mu))
# kernel support parameter
k <- 1
H <- seq((max(y) - min(y)) / 200, (max(y) - min(y)) / 2, length.out = 50)
hcv <- cv_bandwidth(kernel = "optimal", y, h = H, k = k)
Discrete binomial kernel
Description
Discrete binomial kernel
Usage
discrete_binomial(x, z, h)
Arguments
x |
the target point at which the density is calculated |
z |
the vector of observations |
h |
the bandwidth (or smoothing parameter) which should match the condition 0<= h < 1 |
Value
Returns the value of the associated kernel function according to the target x and the bandwidth h.
Examples
# Basic usage of discrete_binomial() to compute a Discrete Binomial Kernel
discrete_binomial(x = 25, z = 1:50, h = 0.5)
Discrete Epanechnikov kernel
Description
Discrete Epanechnikov kernel
Usage
discrete_epanech(x, z, h)
Arguments
x |
the target point at which the density is calculated |
z |
the vector of observations |
h |
the bandwidth (or smoothing parameter) |
Value
Returns the value of the associated kernel function according to the target x and the bandwidth h.
Examples
# Basic usage of discrete_epanech() to compute a discrete Epanechnikov kernel
discrete_epanech(x = 25, z = 1:50, h = 20)
Discrete kernel function
Description
Discrete kernel function
Usage
discrete_kernel(
kernel = c("optimal", "triang", "epanech", "binomial"),
x,
z,
h,
k = NULL
)
Arguments
kernel |
the type of kernel. Currently supported kernels are limited to: "optimal", "triang", "epanech" and "binomial" |
x |
the target point at which the density is calculated |
z |
the vector of observations |
h |
the bandwidth (or smoothing parameter) |
k |
Optional: the integer (positive) parameter that defined the support of the kernel function (corresponds to parameter 'a' for triangular kernel). It is only used for optimal and triangular kernel |
Value
Returns the value of the associated kernel function
See Also
discrete_optimal(), discrete_triang(), discrete_epanech(),
discrete_binomial() which this function wraps.
Examples
discrete_kernel(kernel = "optimal", x = 25, z = 1:50, h = 0.9, k = 20)
discrete_kernel(kernel = "triang", x = 25, z = 1:50, h = 10, k = 20)
discrete_kernel(kernel = "epanech", x = 25, z = 1:50, h = 20)
discrete_kernel(kernel = "binomial", x = 25, z = 1:50, h = 0.5)
Discrete optimal kernel
Description
Discrete optimal kernel
Usage
discrete_optimal(x, z, h, k)
Arguments
x |
the target point at which the density is calculated |
z |
the vector of observations |
h |
the bandwidth (or smoothing parameter), which should match the condition (3 / 5) * (1 - 1 / k)) < h < 1 |
k |
the integer (positive) parameter that defined the support of the kernel function |
Value
Returns the value of the associated kernel function according to the target x and the bandwidth h.
Examples
discrete_optimal(x = 25, z = 1:50, h = 0.9, k = 20)
Discrete triangular kernel
Description
Discrete triangular kernel
Usage
discrete_triang(x, z, h, a)
Arguments
x |
the target point at which the density is calculated |
z |
the vector of observations |
h |
the bandwidth (or smoothing parameter) |
a |
the integer (positive) parameter that defined the support of the kernel function |
Value
Returns the value of the associated kernel function according to the target x and the bandwidth h.
Examples
# Basic usage of discrete_triang() to compute a Discrete triangular kernel
discrete_triang(x = 25, z = 1:50, h = 10, a = 20)
Discrete Kernel Density Estimator
Description
Discrete Kernel Density Estimator
Usage
estim_kernel(
kernel = c("optimal", "triang", "epanech", "binomial"),
x,
h,
v,
k = NULL
)
Arguments
kernel |
the type of kernel. Currently supported kernels are limited to: "optimal", "triang", "epanech" and "binomial" |
x |
the list of target points at which the density is calculated |
h |
the bandwidth (or smoothing parameter) |
v |
the vector of observations |
k |
Optional: the integer (positive) parameter that defined the support of the kernel function (corresponds to parameter 'a' for triangular kernel). It is only used for optimal and triangular kernel |
Value
The estimated discrete kernel density values
Examples
n <- 250
mu <- 2 # Mean
x <- 0:10 # target values
y <- sort(rpois(n, mu)) # simulated Poisson observations
# kernel parameters
kernel <- "optimal"
k <- 1
# Cross Validation
H <- seq((max(y) - min(y)) / 200, (max(y) - min(y)) / 2, length.out = 50)
hcv <- cv_bandwidth(kernel = kernel, y, h = H, k = k)
# Kernel estimation
fn_opt_k <- estim_kernel(kernel = kernel, x = x, h = hcv, v = y, k = k)
Fish dataset from the SIMTAP project
Description
The SIMTAP project (Self-sufficient Integrated Multi-Trophic AquaPonic systems) aimed to develop sustainable aquaculture production system that, in particular, contributes to reduce fish feed inputs and resources consumption. We used data from an experiment in which gilthead seabream (sparus aurata) were stocked in 1.6 m3 tanks at a density of 1.5 kg·m-3 . Fish were reared for 46 days in a single recirculating aquaculture system composed of three rearing tanks. At the beginning of the experiment, a number n =200 of the fish were individually weighed (dg), and their length at the caudal fork (mm) was measured.
Usage
fish_data
Format
fish_data
A data frame with 200 rows and 2 columns:
- length
Length in mm
- weight
Weight in dg
...