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<p>In this paper, we intend to estimate the stress-strength reliability parameter of a one-parameter exponential distribution when the sample sizes for stress and strength variables are unequal. Consideration is given to the weighted squared-error loss and non-linear cost functions while estimating the reliability parameter using its maximum likelihood (ML) estimator. The aim is to minimize the expected loss and achieve the minimum risk corresponding to the associated optimal fixed-sample sizes. We establish that no fixed-sample size procedure can solve this estimation problem and propose a two-stage sequential sampling technique for this purpose. Moreover, we deduce several exact and asymptotic properties associated with the corresponding stopping rules. All theoretical findings are validated via large-scale simulations under different parameter configurations. We also present a real-data illustration to complement the practical importance of the proposed estimation strategy.</p>

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Minimum risk two-stage sequential point estimation of \(R=\mathbb {P}(X for a one-parameter exponential distribution with unequal sample sizes

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Neeraj Joshi,
  • Anirban Chakraborty

摘要

In this paper, we intend to estimate the stress-strength reliability parameter of a one-parameter exponential distribution when the sample sizes for stress and strength variables are unequal. Consideration is given to the weighted squared-error loss and non-linear cost functions while estimating the reliability parameter using its maximum likelihood (ML) estimator. The aim is to minimize the expected loss and achieve the minimum risk corresponding to the associated optimal fixed-sample sizes. We establish that no fixed-sample size procedure can solve this estimation problem and propose a two-stage sequential sampling technique for this purpose. Moreover, we deduce several exact and asymptotic properties associated with the corresponding stopping rules. All theoretical findings are validated via large-scale simulations under different parameter configurations. We also present a real-data illustration to complement the practical importance of the proposed estimation strategy.