Sequential point and interval estimation of scale parameter of exponential distribution

摘要

Sequential fixed-width confidence intervals are obtained for thescale parameterσwhen the location parameterθof the negative exponentialdistribution is unknown. Exact expressions for the stopping time and theconfidence coefficient associated with the sequential fixed-width interval arederived. Also derived is the exact expression for the stopping time of sequentialpoint estimation with quadratic loss and linear cost. These are numericallyevaluated for certain nominal confidence coefficients, widths of the interval andcost functions, and are compared with the second order asymptotic expressions.