Check the sensitivity of MLE

> binom.mle.vin <- function(param, data) {
+     k <- param[1]
+     p <- param[2]
+     loglik <- sum(data) * log(p) + (k * 5 - sum(data)) * log(1 -
+         p) + sum(log(choose(k, data)))
+     return(-loglik)
+ }

Starting with the following data

> data <- c(16, 18, 22, 25, 27)
> optim(par = c(40, 0.1), fn = binom.mle.vin, method = "L-BFGS-B",
+     lower = c(27, 1e-06), upper = c(1100, 0.99999), data = data)$par
[1] 98.4332928  0.2194390

Tweak the data with just one addition

> data <- c(16, 18, 22, 25, 28)
> optim(par = c(40, 0.1), fn = binom.mle.vin, method = "L-BFGS-B",
+     lower = c(27, 1e-06), upper = c(1100, 0.99999), data = data)$par
[1] 180.6084976   0.1207055

With the change of 1 element from 27 to 28, the MLE estimate of total trials has shot up from 98 to 180

Parameters are extremely sensitive.