statwonk

library(tidyverse)
# https://www.kellogg.northwestern.edu/faculty/weber/decs-430/Notes%20on%20the%20Poisson%20and%20exponential%20distributions.pdf
# http://www.mscs.mu.edu/~jsta/issues/11(3)/JSTA11(3)p2.pdf

# Case 1: memoryless intra-arrival times. They're not correlated.
tibble::tibble(
  durations_between = rexp(3e4, rate = 20)
) %>%
  mutate(time = cumsum(durations_between)) %>%
  mutate(time_interval = cut(time, breaks = seq(0, 1e4, 1), labels = FALSE)) %>%

statwonk

library(tidyverse)
library(brms)
library(tidybayes)
library(ggthemes)

# Simulation settings
innings <- 9
games <- 162
number_of_opposing_pitchers <- 20 # purposly set low to illustrate variation
opposing_pitchers <- rnorm(number_of_opposing_pitchers, sd = 0.5) # a set of opposing pitcher effects

statwonk

# install.packages("countreg", repos="http://R-Forge.R-project.org")
# https://www.fromthebottomoftheheap.net/2016/06/07/rootograms/
# https://channel9.msdn.com/Events/useR-international-R-User-conferences/useR-International-R-User-2017-Conference/countreg-Tools-for-count-data-regression
library(countreg)

rzinbinom(3e3, size = 4, mu = 20, pi = 0.05) -> x
table(x)
hist(x, col = "orange")

rootogram(glm(x ~ 1, family = "poisson")) # zeros under fit

statwonk

library(tidyverse)
expand.grid(
  risk = seq(0.001, 0.02, 0.001),
  units_of_exposure = seq_len(24*7)
) %>% as_tibble() %>%
  mutate(total_risk = map2_dbl(risk, units_of_exposure, ~ 1 - (1 - .x)^(.y))) %>%
  ggplot(aes(x = risk, y = units_of_exposure)) +
  geom_raster(aes(fill = total_risk), alpha = 0.90) +
  scale_fill_gradient2(name = "Total chance", 
                       low = "white", mid = "white", high = "purple4", midpoint = 0.5,

statwonk

# https://news.ycombinator.com/item?id=20356610
# chance of the cluster size being >5 when we can cluster events within a one-week period 
# and the rate of events is one every 2 months (debatable, but feels right to me)?

# My re-write:
# probability of more than four outages in a given week given a rate of every other month
# _assuming_: totally unrelated infra (none share AWS, etc.)
ppois(4, lambda = 1/2/4.5, lower.tail = FALSE) # ~ 1/7M chance.

# Given that we've observed five in one-week, 

statwonk

library(tidyverse)
library(survival)

rweibull_cens <- function(n, shape, scale) {
  # http://statwonk.com/weibull.html
  a_random_death_time <- rweibull(n, shape = shape, scale = scale) 
  a_random_censor_time <- rweibull(n, shape = shape, scale = scale)
  observed_time <- pmin(a_random_censor_time, a_random_death_time)
  censor <- observed_time == a_random_death_time
  tibble(time = observed_time, censor = censor)

statwonk

library(brms)
library(tidybayes)

N <- 1e3
number_of_groups <- 12
group_means <- rnorm(number_of_groups)

tibble(obs = seq_len(N)) %>%
  mutate(group = sample(seq_len(number_of_groups), n(), replace = TRUE),
         contribution = group_means[group],

statwonk

library(tidyverse)

tibble(boot = seq_len(1e2)) %>%
  mutate(prediction_intervals = map(boot, function(i) {
    rpois(100, 10) -> x
    
    (sum(x[6:100]) -> total_oracle)
    
    # Given the first five, what can we say about the sum of 95 more?
    x[1:5] -> first_five

statwonk

library(tidyverse)
plot.new()
par(bg = "black")
plot(density(rnorm(1e6)), col = "deeppink", lwd = 1,
     xlab = "", ylab = "", main = "Normal distribution", axes = FALSE)
seq(1, 10, 0.05) %>%
  map(function(x){ rnorm(1e5, 0, x)}) %>%
  map(function(x) { density(x) %>%
      lines(col = colors() %>% Filter(function(.x) grepl("pink", .x), .) %>% sample(1),
            lwd = sample(seq(0.1, 0.1, 0.01), 1),

statwonk

library(tidyverse)
plot.new()
par(bg = "black")
plot(density(rbeta(1e6, 50, 50)), col = "pink3", lwd = 1, ylim = c(0, 8),
     xlab = "", ylab = "", main = "Beta distribution", axes = FALSE,
     col.main = 'white')
map2(c(seq(1, 49, 1), 50),
     c(seq(1, 49, 1), 50),
     function(x, y){ message(x,y);rbeta(1e6, x + 1, y + 1)}) %>%
  map(function(x) { density(x) %>%