# What is the meaning of monotone hazard rate (MHR) distribution?

It might be somewhat irrelevant to this forum but I think that many people here are familiar with this concept. I have seen that many papers assume that customers' valuation ($$F$$) is a monotone hazard rate (MHR) distribution, that is, the hazard rate $$\frac{f(v)}{1-F(v)}$$ is non-decreasing in $$v$$. What does this assumption implicate from a business perspective? Moreover, what is the impact of this assumption on optimization procedures?

Many papers in Revenue Management and Dynamic Pricing use hazard rate, but what does it mean in these contexts?

• I would be grateful if there is anybody who can explain this concept? Jun 23 '20 at 7:41
• In the denominator, $F(c)$ should be $F(v)$, right? Jun 23 '20 at 14:54
• please have a look on this document. Jun 23 '20 at 18:32

For a Poisson process the rate of events is constant. The distribution of time between events in the Poisson process is exponential with $$F(v)=1-e^{-\lambda v}$$ for $$v\ge 0$$ which gives the hazard rate $$\lambda$$. So a non-constant hazard rate can be seen as a way of comparing with a Poisson process, an increasing hazard rate means the events come faster and faster, like delinquences in a financial crisis ... For some more examples see this posts over at Cross Validated: Examples of non-monotone hazard functions and New Better than Used.