inst/doc/graph_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
)

## -----------------------------------------------------------------------------
oldpar <- par(mfrow = c(2, 2), mar = c(1, 1, 1, 1)) # 2 x 2 pictures on one plot
# 1,1 - Optimal (k=1, h) and Epanechnikov (h=1)
plot(
  x = z,
  # y = K_opt[, 1],
  xlab = "z",
  ylab = "Probability",
  ylim = c(0, 1),
  main = "Optimal (k=1, h) and Epanechnikov (h=1)",
  type = "o",
  pch = 1,
  # Symbol
  lty = 1,
  # Line type
  lwd = 2,
  # Line width
  cex = 1.6,
  # Magnification factor
  cex.axis = 1.2,
  # Magnification factor for axis
  cex.lab = 1.2,
  # Magnification factor for label
)

lines(
  z,
  K_opt[, 2],
  type = "o",
  pch = 2,
  # Symbol
  lty = 2,
  # Line type
  lwd = 2,
  # Line width
  col = "grey",
)

lines(
  z,
  K_opt[, 3],
  type = "o",
  pch = 3,
  lty = 3,
  lwd = 2
)


lines(
  z,
  K_epan[, 1],
  type = "o",
  pch = 4,
  lty = 4,
  lwd = 2,
  col = "grey"
)

legend(
  0,
  1,
  c("Opt. h=0.2", "Opt. h=0.7", "Opt. h=0.95", "Epan. h=1"),
  lty = c(1, 2, 3, 4),
  pch = c(1, 2, 3, 4),
  col = c("black", "grey", "black", "grey"),
  lwd = c(2, 2, 2, 2),
  cex = 1.2
)



# Triangular (a=1, h) and Epanechnikov (h=1)
z <- 0:10
x <- 5
a <- 1
h <- c(0.2, 0.7, 0.95)
K_trg <- matrix(0, length(z), length(h))
for (i in 1:length(h))
{
  K_trg[, i] <- discrete_triang(x, z, h[i], a)
}

plot(
  z,
  K_trg[, 1],
  xlab = "z",
  ylab = "Probability",
  main = "Triangular (a=1, h) and Epanechnikov (h=1)",
  ylim = c(0, 1),
  type = "o",
  pch = 1,
  lty = 1,
  lwd = 2,
  cex = 1.6,
  cex.axis = 1.2,
  cex.lab = 1.2
)

lines(
  z,
  K_trg[, 2],
  type = "o",
  pch = 2,
  lty = 2,
  lwd = 2,
  col = "grey"
)

lines(
  z,
  K_trg[, 3],
  type = "o",
  pch = 3,
  lty = 3,
  lwd = 2
)

lines(
  z,
  K_epan[, 1],
  type = "o",
  pch = 4,
  lty = 4,
  lwd = 2,
  col = "grey"
)

legend(
  0,
  1,
  c("Triang. h=0.2", "Triang. h=0.7", "Triang. h=0.95", "Epan. h=1"),
  lty = c(1, 2, 3, 4),
  pch = c(1, 2, 3, 4),
  col = c("black", "grey", "black", "grey"),
  lwd = c(2, 2, 2, 2),
  cex = 1.2
)

#  Optimal (k=2, h) and Epanechnikov (h=2)
# p=k=2
# opt
z <- 0:10
x <- 5
k <- 2
h <- c(0.5, 0.7, 0.95)
K_opt <- matrix(0, length(z), length(h))
for (i in 1:length(h))
{
  K_opt[, i] <- discrete_optimal(x, z, h[i], k)
}


plot(
  z,
  K_opt[, 1],
  xlab = "z",
  ylab = "Probability",
  ylim = c(0, 1),
  main = "Optimal (k=2, h) and Epanechnikov (h=2)",
  type = "o",
  pch = 1,
  lty = 1,
  lwd = 2,
  cex = 1.6,
  cex.axis = 1.2,
  cex.lab = 1.2
)

lines(
  z,
  K_opt[, 2],
  type = "o",
  pch = 2,
  lty = 2,
  lwd = 2,
  col = "grey"
)

lines(
  z,
  K_opt[, 3],
  type = "o",
  pch = 3,
  lty = 3,
  lwd = 2
)

lines(
  z,
  K_epan[, 2],
  type = "o",
  pch = 4,
  lty = 4,
  lwd = 2,
  col = "grey"
)

legend(
  0,
  1,
  c("Opt. h=0.5", "Opt. h=0.7", "Opt. h=0.95", "Epan. h=2"),
  lty = c(1, 2, 3, 4),
  pch = c(1, 2, 3, 4),
  col = c("black", "grey", "black", "grey"),
  lwd = c(2, 2, 2, 2),
  cex = 1.2
)

# Triangular (a=2, h) and Epanechnikov (h=2)
# triangular
z <- 0:10
x <- 5
a <- 2
h <- c(0.5, 0.7, 0.95)
K_trg <- matrix(0, length(z), length(h))
for (i in 1:length(h))
{
  K_trg[, i] <- discrete_triang(x, z, h[i], a)
}


plot(
  z,
  K_trg[, 1],
  xlab = "z",
  ylab = "Probability",
  main = "Triangular (a=2, h) and Epanechnikov (h=2)",
  ylim = c(0, 1),
  type = "o",
  pch = 1,
  lty = 1,
  lwd = 2,
  cex = 1.6,
  cex.axis = 1.2,
  cex.lab = 1.2
)

lines(
  z,
  K_trg[, 2],
  type = "o",
  pch = 2,
  lty = 2,
  lwd = 2,
  col = "grey"
)

lines(
  z,
  K_trg[, 3],
  type = "o",
  pch = 3,
  lty = 3,
  lwd = 2
)

lines(
  z,
  K_epan[, 2],
  type = "o",
  pch = 4,
  lty = 4,
  lwd = 2,
  col = "grey"
)

legend(
  0,
  1,
  c("Triang. h=0.5", "Triang. h=0.7", "Triang. h=0.95", "Epan. h=2"),
  lty = c(1, 2, 3, 4),
  pch = c(1, 2, 3, 4),
  col = c("black", "grey", "black", "grey"),
  lwd = c(2, 2, 2, 2),
  cex = 1.2
)

# Restore option
par(oldpar)