Journal
| Title | Two-Stage Sequential Interval Estimation of Functions of the Exponential Scale Parameters Posted by Bernadette Tubo |
| Authors | Tubo, Bernadette F. ; Polestico, Daisy Lou L. and Serquiña, Ruth P. |
| Publication date | 2020 |
| Journal | Asia Pacific Journal of Science, Mathematics and Engineering |
| Volume | 6 |
| Issue | 2 |
| Pages | 24-27 |
| Publisher | ISSN:2244-5471 |
| 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¸ 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_d<infinity)=1. Moreover, we also provide the coverage probability of the interval estimates I_n guaranteeing asymptotic consistency for the parameter theta. Performances of the proposed two-stage methodology is illustrated via simulation using the R programming language on a parameter of the forms theta=(sigma_1/sigma_2)^r and theta=|sigma_1-sigma_2 |^r for r>0. Simulation results show that the proposed two-stage procedure is asymptotically consistent. |
| Index terms / Keywords | two-stage sequential procedure, confidence interval, stopping rule, exponential distribution |