MHR, Regular Distributions and Myerson’s Lemma Monotone Hazard
Rate (MHR) distributions and its superclass regular
distributions keep appearing in the Mechanism Design literature
and this is due to a very good reason: they are the class of
distributions for which Myerson’s Optimal Auction is simple and
natural. Let’s brief discuss some properties of those
distributions. First, two definitions: - Hazard rate of a
distribution : - Myerson virtual value of a distribution : We
can interpret the hazard rate in the following way: think of as
a random variable that indicates the time that a light bulb will
take to extinguish. If we are in time and the light bulb hasn’t
extinguished so far, what is the probability it will extinguish
in the next time: We say that a distribution is monotone hazard
rate, if is non-decreasing. This is very natural for light
bulbs, for example. Many of the distributions that we are used
to are MHR, for example, uniform, exponential and normal. The
way that I like to think about MHR distri