Illustration of negative binomial.

negative_binomial.R

#' Graph of number of tries needed to obtain K successes.
#' @param K number of studies.
#' @return NULL.

plotter = function(K){
  kk = 0:(K*70)
  plot(kk + K, dnbinom(kk, K, 0.05), bty = "l", type = "b", pch = 20,
       xlab = "Number of studies", 
       ylab = "Probability",
       main =  paste0("Number of studies before ", K, " successes"))
  abline(v = 0.95/0.05*K + K, lty = 2)
  abline(v = floor(0.95/0.05*(K-1) + K), lty = 2, col = "red")
  abline(v = qnbinom(0.5, K, 0.05) + K, lty = 2, col = "blue")
  legend("topright", col = c("black", "blue", "red"),
         lty = c(2, 2, 2), legend = c(
           paste0("Mean: ", 0.95/0.05*K + K),
           paste0("Mode: ", floor(0.95/0.05*(K-1) + K)),
           paste0("Median: ", qnbinom(0.5, K, 0.05) + K)
         ), bty = "n")  
}

plotter(2)