Introduction

book/P1C2_preview.qmd

@@ -6,6 +6,6 @@ abstract: TODO (150-200 WORDS)
 {{< include _macros.tex >}}
 :::
 
-# MLSA From Start to Finish
+# MLSA From Start to Finish {#sec-mlsa}
 
 {{< include _soon.qmd >}}

book/P1C4_survival.qmd

@@ -37,8 +37,7 @@ In practice the differences are often blurred as time-measurement will naturally
 Also discrete-time methods are often applied to continuous time data and vice versa.
 It is nevertheless important to make the distinction as it informs mathematical treatment and definition of the different quantities introduced below.
 
-
-### Continuos Time {#sec-distributions-continuous}
+### Continuous Time {#sec-distributions-continuous}
 
 For now, assume a continuous, positive, random variable $Y$ taking values in (t.v.i.) $\NNReals$.
 A standard representation of the distribution of $Y$ is given by the probability density function (pdf), $f_Y: \NNReals \rightarrow \NNReals$, and cumulative distribution function (cdf), $F_Y: \NNReals \rightarrow [0,1]; (\tau) \mapsto P(Y \leq \tau)$.

book/experiments/code.R

@@ -5,6 +5,19 @@ remotes::install_github("mlr-org/paradox", ref = 'v0.11.1', upgrade = "never")
 library(ggplot2)
 theme_set(theme_bw())
 
+library(distr6)
+library(ggplot2)
+g = dstr("Gompertz", shape = 2, decorators = "ExoticStatistics")
+t = seq.int(0, 1.5, length.out = 100)
+d = data.frame(t = t, fun = factor(rep(c("Density", "Hazard", "Cumulative Density", "Survival"), each = 100), levels = c("Density", "Hazard", "Cumulative Density", "Survival")), y = c(g$pdf(t), g$hazard(t), g$cdf(t), g$survival(t)))
+g = ggplot(d, aes(x = t, y = y, color = fun)) +
+  geom_line() +
+  facet_wrap(~fun, scales = "free", nrow = 2) +
+  theme_bw() +
+  theme(legend.position = "n")
+ggsave("book/Figures/introduction/gompertz.png", g, height = 3, units = "in",
+  dpi = 600)
+
 ## Ranking
 rm(list = ls())
 library(dplyr)