Googling "maximum likelihood binomial" will give you several direct analytical descriptions of this. Alternatively, you can think of a binomial rv as the sum of n Bernoulli rv's. So, N trials of a binomial is essentially n*N trials of a Bernoulli, and the argument given in this video applies.
The harder problem is ML binomial estimation when neither n nor p is known. I have not seen how to come up with the estimator analytically. Thankfully, n would usually be known in applications.
Googling "maximum likelihood binomial" will give you several direct analytical descriptions of this. Alternatively, you can think of a binomial rv as the sum of n Bernoulli rv's. So, N trials of a binomial is essentially n*N trials of a Bernoulli, and the argument given in this video applies.
The harder problem is ML binomial estimation when neither n nor p is known. I have not seen how to come up with the estimator analytically. Thankfully, n would usually be known in applications.
MathHolt 1 year ago
i would be so grateful if you could explain me the ML function and the estimator for p in a binomial case!
whattheh3ll 1 year ago