# A Poisson Fishing Model

### Thomas S. Ferguson

#### Abstract:

A fishing model of Starr, Wardrop, and Woodroofe is related to the
sequential search model of Cozzolino. The latter is generalized to
allow an arbitrary joint distribution of capture times and fish sizes.
There are a random number, M, of fish in a pond. Each fish has a
random size, X (with finite variance), and a random time of being
caught, Y>0 (with finite mean). It is assumed that given M=m,
(X(1),Y(1)), . . ., (X(m),Y(m)) are i.i.d.. The problem is to choose a
stopping time, T, to maximize the sum of the sizes of the fish
caught by time T minus c(T), a cost of time. Implications to the
foraging models of Oaten and Green and to debugging software are
indicated.