| Abstract |
Let X_1,X_2,...,X_n and Y_1,Y_2,,...,Y_n be random samples from two exponential populations, with scale parameters, sigma_1 and sigma_2, respectively. This paper considers a two-stage sequential procedure to construct fixed-width confidence intervals I_n for functions of the exponential scale parameters of the form theta=h(sigma_1, sigma_2) where h is a real-valued, three-times continuously differential function defined on R_+^2. A two-stage sequential procedure is proposed for the estimation of theta脗赂 through the stopping rules m_d and N_d defined in equations (3) and (4), respectively. Under the assumption that sigma_1 > sigma_L and sigma_2 > sigma_G, where sigma_L, sigma_G>0 are lower bounds known to the experimenter from past experiences, we have shown that the stopping rule N_d is a good estimate of the optimal sample size n^*defined in (2). We have shown that the proposed two-stage sequential procedure will eventually stop with probability 1, that is, P(N_d0. Simulation results show that the proposed two-stage procedure is asymptotically consistent. |
Mindanao State
University - Iligan Institute of Technology