Whenever I look at password entropy, the only equation I ever see is E = log2(R)*L, or alternatively E = log2(R^L), where E is password entropy, R is the range of available characters, and L is the password length.
I was wondering if there are any alternate equations for calculating entropy which factor weak passwords into the equation. For instance, passwords with sequential characters (0123456789), common phrases (logmein), repeating words (happyhappy), or words with numbers appended (password1) would all receive a lower entropy grade due to their various shortcomings.
Does such an equation exist? If so, is it commonly used in the security field, or do people tend to stick with the "standard equation?"