Sequential point and interval estimation of scale parameter of exponential distribution

Abstract

Sequential fixed-width confidence intervals are obtained for the scale parameter σ when the location parameter θ of the negative exponential distribution is unknown. Exact expressions for the stopping time and the confidence coefficient associated with the sequential fixed-width interval are derived. Also derived is the exact expression for the stopping time of sequential point estimation with quadratic loss and linear cost. These are numerically evaluated for certain nominal confidence coefficients, widths of the interval and cost functions, and are compared with the second order asymptotic expressions.

Keywords

• stopping time
• exponential distribution
• sequential estimation of scale parameter.