A two-parameter random walk with approximate exponential probability distribution
Erik Van der Straeten, Jan Naudts
Abstract
We study a non-Markovian random walk in dimension 1. It depends on two parameters epsr and epsl, the probabilities to go straight on when walking to the right, respectively to the left. The position x of the walk after n steps and the number of reversals of direction k are used to estimate epsr and epsl. We calculate the joint probability distribution pn(x,k) in closed form and show that, approximately, it belongs to the exponential family.
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