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In optical communication systems, photons are lost due to the attenuation of the transmission medium. To efficiently implement quantum information protocols, we need to be able to precisely describe such processes. In this paper, we propose statistical methods to estimate the attenuation coefficient of the fiber link. By following the Beer–Lambert law, we utilize the properties of the exponential distribution to estimate the rate parameter based on observable data. In particular, we determine the explicit forms of unbiased estimators that are suitable for censored (truncated) sets of data. Moreover, we focus on minimum-variance methods that ensure a reliable estimation of the attenuation coefficient.