An Estimation Problem with Poisson Processes

For n independent Poisson processes such that the i th process has intensity function lM_i(t) =δ_iρ(t; α) we consider estimation of p(t; α) =∫_oρ:(u; α) du. Two procedures are developed, one using exact arrival times, the other using categorical arrival times. Two instances where p(t; α) =p(α t) are investigated further. An example applying the methodology to the active life of a judicial opinion is described.