Comparing MOM, MLE, & MAP:
- MOM: Based on the assumption that sample moments should provide good estimates of the corresponding population moments. Older, classic method. May be less efficient.
- MLE: Trying to find the values of the parameters which would have most likely produced the observed data. One way to maximize the likelihood equation is through taking the derivative.
- MAP: This is the same thing as MLE, except that it includes a distribution of prior knowledge, Bayesian style.
CDF vs PPF:
- CDF = Given an x value, what is the probability that the random variable takes a value less than or equal to that x value? e.g., What is the probability that the random variable is less than or equal to 5?
- PPF = Given a cumulative probability, what is the x value that corresponds to that? e.g., There is a 40% probability that the random variable is less than or equal to what x value?