178 lines
5.3 KiB
R
178 lines
5.3 KiB
R
# 1. Load functions and Libraries ----------------------------------------------
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source("./R/graphon_distribution.R")
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# 2. Set constants -------------------------------------------------------------
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withr::with_seed(42) # set seed in a local environment
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a0 <- c(0, 0)
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a1 <- c(1.0)
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a2 <- c(0.5, -0.3)
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N <- 400 # number of samples for X
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X1 = matrix(rnorm(N))
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X2 = matrix(rnorm(2 * N), ncol = 2)
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# 3. Normally distributed v's --------------------------------------------------
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## 3.1 Plot a = 0 ==============================================================
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# In this section we plot the conditional density p(u | x) for v ~ N(0,1) and
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# a = (0, 0)
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p1 <- create_cond_density(a0, dnorm, pnorm, X2)
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givenX <- c(0, 0)
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p1_plot <- \(x) p1(x, givenX)
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plot.function(p1_plot, xlab="u", ylab="p(u |x) ")
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title(main=expression("Conditional density for" ~ v %~% N(0, 1)), line=2)
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title(
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main = bquote(
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a == (.(paste(a0, collapse = ", "))) ~ "," ~
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N == .(N) ~ "," ~
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x == (.(paste(givenX, collapse = ", ")))
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),
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line = 1,
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cex = 0.65
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)
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## 3.2 Plot a != 0, X != 0 =====================================================
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p2 <- create_cond_density(a2, dnorm, pnorm, X2)
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givenX <- c(-0.5, 0.5)
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p2_plot <- \(x) p2(x, givenX)
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plot.function(p2_plot, xlab="u", ylab="p(u |x) ")
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title(main=expression("Conditional density for" ~ v %~% N(0, 1)), line=2)
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title(
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main = bquote(
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a == (.(paste(a2, collapse = ", "))) ~ "," ~
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N == .(N) ~ "," ~
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x == (.(paste(givenX, collapse = ", ")))
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),
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line = 1,
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cex = 0.65
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)
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## 3.3 Plot one dimensional X_i ================================================
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p3 <- create_cond_density(a1, dnorm, pnorm, X1)
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givenX <- c(-0.5)
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p3_plot <- \(x) p3(x, givenX)
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plot.function(p3_plot, xlab="u", ylab="p(u |x) ")
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title(main=expression("Conditional density for" ~ v %~% N(0, 1)), line=2)
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title(
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main = bquote(
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a == (.(paste(a1, collapse = ", "))) ~ "," ~
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N == .(N) ~ "," ~
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x == (.(paste(givenX, collapse = ", ")))
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),
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line = 1,
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cex = 0.65
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)
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## 3.4 Plot v ~ N(0, 2) ========================================================
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dens_func <-\(x) dnorm(x, sd=sqrt(2))
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cdf <- \(x) pnorm(x, sd=sqrt(2))
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p4 <- create_cond_density(a1, dens_func, cdf, X1)
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givenX <- c(-0.5)
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p4_plot <- \(x) p4(x, givenX)
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plot.function(p4_plot, xlab="u", ylab="p(u |x) ")
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title(main=expression("Conditional density for" ~ v %~% N(0, 2)), line=2)
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title(
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main = bquote(
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a == (.(paste(a1, collapse = ", "))) ~ "," ~
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N == .(N) ~ "," ~
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x == (.(paste(givenX, collapse = ", ")))
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),
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line = 1,
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cex = 0.65
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)
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# 4. Expontial distribution for v's --------------------------------------------
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## 4.1 One dimensional X_i =====================================================
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# This example has a jump in [0.14, 0.15].
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# The zero can not be explained and it's not a probability as:
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# integrate(p5_plot, 0.15, 1, subdivisions = 500)
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# => 0.952492 with absolute error < 0.00011
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lambda <- 1.0
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p5 <- create_cond_density(a1, dexp, pexp, X1)
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givenX <- c(-0.5)
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p5_plot <- \(x) p5(x, givenX)
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plot.function(p5_plot, xlab="u", ylab="p(u |x) ")
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title(main=expression("Conditional density for" ~ v %~% Exp(1)), line=2)
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title(
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main = bquote(
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a == (.(paste(a1, collapse = ", "))) ~ "," ~
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N == .(N) ~ "," ~
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x == (.(paste(givenX, collapse = ", ")))
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),
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line = 1,
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cex = 0.65
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)
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## 4.2 Two dimensional X_i =====================================================
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lambda <- 1.0
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p6 <- create_cond_density(a2, dexp, pexp, X2)
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givenX <- c(-0.5)
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p6_plot <- \(x) p6(x, givenX)
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plot.function(p6_plot, xlab="u", ylab="p(u |x) ")
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title(main=expression("Conditional density for" ~ v %~% Exp(1)), line=2)
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title(
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main = bquote(
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a == (.(paste(a2, collapse = ", "))) ~ "," ~
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N == .(N) ~ "," ~
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x == (.(paste(givenX, collapse = ", ")))
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),
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line = 1,
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cex = 0.65
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)
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## 4.3 Higher Rate of exponential distribtion ==================================
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lambda <- 2.0
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dens_func <- \(x) dexp(x, rate=lambda)
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cdf <- \(x) pexp(x, rate=lambda)
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p7 <- create_cond_density(a2, dens_func, cdf, X2)
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givenX <- c(-0.5, 0.5)
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p7_plot <- \(x) p7(x, givenX)
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plot.function(p7_plot, xlab="u", ylab="p(u |x) ")
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title(main=expression("Conditional density for" ~ v %~% Exp(2.0)), line=2)
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title(
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main = bquote(
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a == (.(paste(a2, collapse = ", "))) ~ "," ~
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N == .(N) ~ "," ~
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x == (.(paste(givenX, collapse = ", ")))
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),
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line = 1,
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cex = 0.65
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)
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# 5. Uniform Distribution ------------------------------------------------------
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## Two dimensional X_i =========================================================
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p8 <- create_cond_density(a2, dunif, punif, X2)
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givenX <- c(-0.5, 0.5)
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p8_plot <- \(x) p8(x, givenX)
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plot.function(p8_plot, xlab="u", ylab="p(u |x) ")
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title(main=expression("Conditional density for" ~ v %~% U(0,1)), line=2)
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title(
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main = bquote(
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a == (.(paste(a2, collapse = ", "))) ~ "," ~
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N == .(N) ~ "," ~
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x == (.(paste(givenX, collapse = ", ")))
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),
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line = 1,
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cex = 0.65
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)
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## 5.2 One dimensional X_i =====================================================
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p9 <- create_cond_density(a1, dunif, punif, X1)
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givenX <- c(-0.5)
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p9_plot <- \(x) p9(x, givenX)
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plot.function(p9_plot, xlab="u", ylab="p(u |x) ")
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title(main=expression("Conditional density for" ~ v %~% U(0,1)), line=2)
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title(
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main = bquote(
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a == (.(paste(a1, collapse = ", "))) ~ "," ~
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N == .(N) ~ "," ~
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x == (.(paste(givenX, collapse = ", ")))
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),
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line = 1,
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cex = 0.65
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)
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