Distribution of the maximum of the number of impulses at any instant in a type II counter in a given interval of time

Summary Here we have considered a type II counter in which the inter-arrival times of particles are independent identically distributed random variables following a given distribution. Each particle is assumed to give rise to an impulse and the state of the counter at an instant is defined by the number of impulses present at that instant. Two variations of the model are taken into account depending upon whether the system starts initially with an impulse or not. We have obtained integral equations for the distribution of the maximum of the number of impulses at any instant in a given interval of time for the two models considered. Special cases where the inter-arrival times and the duration of the impulses follow the exponential distribution have also been dealt with. Dedicated to Professor V.Ganapathy Iyer on the occasion of his sixty first birth day.