This function is used in ardipper to determine the bound for
the accept-reject algorithm simulating the non-standard conditional distribution
of \(r_1\).
thresh(k, n1, c2, c3, r2, q1)
numerical value of the upper bound, to be compared with the uniform random draw
current proposal for the number of individuals vanishing between the first and second experiments
first capture population size
number of individuals recaptured during the second experiment
number of individuals recaptured during the third experiment
number of individuals vanishing between the second and third experiments
probability of disappearing from the population
This upper bound is equal to $$\frac{{n_1-c_2 \choose k} {n_1-k \choose c_3+r_2}}{{\bar r\choose k}}$$
ardipper