vignettes/graph_3_kernels.R

In kernopt: Estimating Count Data Distributions with Discrete Optimal Symmetric Kernel

## ----include = FALSE----------------------------------------------------------
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

## ----setup--------------------------------------------------------------------
library(kernopt)

## ----fig.cap='Distribution of discrete symmetric Epanechnikov kernel at the target point $x=5$ for various bandwidth parameters $h$.'----
x <- 5 # Target
z <- 0:10 # Observations (?)
h <- c(1, 2, 3, 4) # Set of Bandwidths
K_epan <- matrix(
  data = 0,
  nrow = length(z),
  ncol = length(h)
)
for (i in 1:length(h))
{
  K_epan[, i] <- discrete_kernel(kernel = "epanech", x, z, h[i])
}
plot(
  z,
  K_epan[, 1],
  xlab = "x",
  ylab = "Probability",
  ylim = c(0, 1),
  pch = 1
)
lines(z, K_epan[, 1], lty = 1)
for (i in 2:length(h))
{
  points(z, K_epan[, i], xlab = "z", pch = i)
  lines(z, K_epan[, i], lty = i)
}
legend(
  "topleft",
  c("h=1", "h=2", "h=3", "h=4"),
  lty = 1:4,
  pch = 1:4,
  cex = 1.6
)

## ----fig.cap="Distribution of discrete symmetric triangular kernel ($a=1$) at the target point $x=5$ for various bandwidth parameters $h$."----
x <- 5
z <- 0:10
h <- c(0.1, 0.4, 1, 2)
a <- 1

K_trg <- matrix(
  data = 0,
  nrow = length(z),
  ncol = length(h)
)

for (i in 1:length(h))
{
  K_trg[, i] <- discrete_kernel(kernel = "triang", x, z, h[i], a)
}
plot(
  z,
  K_trg[, 1],
  xlab = "x",
  ylab = "Probability",
  ylim = c(0, 1),
  pch = 1
)
lines(z, K_trg[, 1], lty = 1)
for (i in 2:length(h))
{
  points(z, K_trg[, i], xlab = "z", pch = i)
  lines(z, K_trg[, i], lty = i)
}
legend(
  "topleft",
  c("h=0.1", "h=0.4", "h=1", "h=2"),
  lty = 1:4,
  pch = 1:4,
  cex = 1.6
)

## ----fig.cap='Distribution of discrete symmetric "optimal" kernel ($k=1$) at the target point $x=5$ for various bandwidth parameters $h$.'----
x <- 5
z <- 0:10
h <- c(0.1, 0.4, 0.7, 0.9)
k <- 1

K_opt <- matrix(
  data = 0,
  nrow = length(z),
  ncol = length(h)
)

for (i in 1:length(h))
{
  K_opt[, i] <- discrete_kernel(kernel = "optimal", x, z, h[i], k)
}
plot(
  z,
  K_opt[, 1],
  xlab = "x",
  ylab = "Probability",
  ylim = c(0, 1),
  pch = 1
)
lines(z, K_opt[, 1], lty = 1)
for (i in 2:length(h))
{
  points(z, K_opt[, i], xlab = "z", pch = i)
  lines(z, K_opt[, i], lty = i)
}
legend(
  "topleft",
  c("h=0.1", "h=0.4", "h=0.7", "h=0.9"),
  lty = 1:4,
  pch = 1:4,
  cex = 1.6
)