In paezha/discrtr: A Companion Package for the Book "Discrete Choice Analysis with 'R'"

knitr::opts_chunk$set(echo = TRUE)

print("¡Hola, Prof. Ortúzar!")

library(dplyr) # A Grammar of Data Manipulation
library(evd) # Functions for Extreme Value Distributions 
library(ggplot2) # Create Elegant Data Visualisations Using the Grammar of Graphics

```rUniform distribution"}

Define a function to return a value of one if

-L > x <= L and zero otherwise

uniform <- function(x, L){ # Logical condition: x greater than minus L and less than L ifelse(x > -L & x <= L, # Value if true 1/(2 * L), # Value if false 0) }

Define parameter L for the distribution

L <- 2

Create a data frame for plotting

The function seq() is used to create a sequence of

values starting at from and ending at to with a

step increase of by

df <- data.frame(x =seq(from = -(L+1), to = L+1, by = 0.01)) %>% # Mutate the data frame to add a new column with the # value of the function mutate(f = uniform(x, L))

Plot

ggplot(data = df, # Map column x in the data frame to the x-axis # and column f to the y-axis aes(x = x, y = f)) + geom_area(fill = "orange", alpha = 0.5) + # Set the limits of the y axis ylim(c(0, 1/(2 * L) + 0.2 * 1/(2 * L))) + # Draw a horizontal line for the x axis geom_hline(yintercept = 0) + # Draw a vertical line for the y axis geom_vline(xintercept = 0) + ylab("f(x)")

```r
(L - (-L)) / (2 * L)

# Define L
L <- 2

# Define an upper limit for calculating the probability
X <- 2

# Create a data frame for plotting the full distribution
df <- data.frame(x =seq(from = -(L + 1), 
                        to = L + 1, 
                        by = 0.01)) %>% 
  # Mutate the data frame to add a new column with the
  # value of the function
  mutate(f = uniform(x, L))

# Create a data frame for plotting the portio of the 
# distribution that is less than X
df_p <- data.frame(x =seq(from = -(L + 1), 
                          to = X, 
                          by = 0.01)) %>% 
  mutate(f = uniform(x, L))

# Plot
ggplot() +
  # Use data frame `df` to plot the full distribution
  geom_area(data = df, 
            # Map column x in the data frame to the x-axis
            # and column f to the y-axis
            aes(x = x, 
                y = f),
            fill = "orange", 
            alpha = 0.5) + 
  # Use data frame `df_p` to plot area under the curve to X
  geom_area(data = df_p, 
            # Map column x in the data frame to the x-axis
            # and column f to the y-axis
            aes(x = x, 
                y = f),
            fill = "orange", 
            alpha = 1) + 
  # Set the limits of the y axis
  ylim(c(0, 
         1/(2 * L) + 0.2 * 1/(2 * L))) + 
  # Draw a horizontal line for the x axis
  geom_hline(yintercept = 0) + 
  # Draw a horizontal line for the y axis
  geom_vline(xintercept = 0) +
  ylab("f(x)")

```rUniform cumulative distribution function"}

Define the cumulative distribution function

punif <- function(x, L){ # Logical statement: x less or equal to -L ifelse(x <= -L, # Value if true 0, # If false, check whether x is between -L and L ifelse(x > -L & x <= L, # Value if true (x + L)/(2 * L), # Value if false 1)) }

Define L

L <- 2

Create a data frame for plotting the cumulative distribution function

df <- data.frame(x =seq(from = -(L+1), to = L+1, by = 0.01)) %>% mutate(f = punif(x, L))

Plot

ggplot(data = df, # Map column x in the data frame to the x-axis # and column f to the y-axis aes(x = x, y = f)) + # Add geometric object of type step to the plot to # plot cumulative distribution function geom_step(color = "orange") + ylim(c(0, 1)) + # Set the limits of the y axis geom_hline(yintercept = 0) + # Add y axis geom_vline(xintercept = 0) + # Add x axis ylab("F(x)") # Label the y axis

```rLinear distribution"}
# Define a function for the linear distribution function
linear <- function(x){
  # Logical statement: x between 0 and 1
  ifelse( x > 0 & x <= 1, 
          # Value if true
          2 * x, 
          # Value if false
          0)
} 

# Create a data frame for plotting
df <- data.frame(x =seq(from = 0, 
                        to = 1, 
                        by = 0.01)) %>% 
  mutate(f = linear(x))

# Plot
ggplot(data = df,
       aes(x = x, 
           y = f)) +
  geom_area(fill = "orange", 
            alpha = 0.5) +
  ylim(c(0, 2)) + 
  geom_hline(yintercept = 0) + 
  geom_vline(xintercept = 0) + 
  ylab("f(x)")

```rLinear cumulative distribution function"}

Define a function for the cumulative distribution

plinear <- function(x){ ifelse(x <= 0, 0, ifelse( x > 0 & x <= 1, x^2, 1)) }

Create a data frame for plotting

df <- data.frame(x =seq(from = -0.2, to = 1.2, by = 0.001)) %>% mutate(f = plinear(x))

Plot

ggplot(data = df, aes(x = x, y = f)) + # Add geometric object of type step to the plot to # to plot cumulative distribution function geom_step(color = "orange") +
ylim(c(0, 1)) + geom_hline(yintercept = 0) + geom_vline(xintercept = 0) + ylab("F(x)")

```rCubic distribution"}
# Define a function
cubic <- function(x) 
  ifelse(x <= 0, 
         0,
         ifelse(x > 0 & x <= 1, 
                4 * x^3, 
                0 ))

# Create a data frame for plotting
df <- data.frame(x =seq(from = 0, 
                        to = 1, 
                        by = 0.01)) %>% 
  mutate(f = cubic(x))

# Plot
ggplot(data = df, 
       aes(x = x, 
           y = f)) +
  geom_area(fill = "orange",
            alpha = 0.5) +
  ylim(c(0, 4)) + 
  geom_hline(yintercept = 0) + 
  geom_vline(xintercept = 0) + 
  ylab("f(x)")

rTriangle function", echo=FALSE} knitr::include_graphics(rep("figures/03-Figure-1.jpg"))

paezha/discrtr documentation built on March 1, 2023, 5:25 p.m.