where is a standard type I extreme value random term. Also, since if , . Then, following the derivation of the Multiple Discrete Continuous Extreme Value (MDCEV) model in Bhat (2005), the probability that the household uses the first Q of K vehicle types (Q ≥ 1) for annual mileages may be written as:
is a standard type I extreme value random term. Also, since 
if 
, 
. Then, following the derivation of the Multiple Discrete Continuous Extreme Value (MDCEV) model in Bhat (2005), the probability that 
may be written as: