Many papers in the microstructure literature assume an order arrival rate of the form
$\lambda^a(\delta) = \lambda^b(\delta) = Ae^{-k\delta}$
That is, an order that's placed $\delta$ away from the mid-price is likely to be executed with probability $Ae^{-k\delta}$. How would you choose k and A given data from a real contract?
In particular, this is used in the seminal paper by Avellanda and Stoikov (http://www.math.nyu.edu/faculty/avellane/HighFrequencyTrading.pdf) in section 2.5