Maximum likelihood estimation of parameters is considered in the situation where a measurement x is taken to mean "x + d." The maximum likelihood estimator for the parameter of the exponential distribution is found for this case and compared with the usual estimator.
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Minton, Paul D. and Seshadri, Vanamamalai
"On the Estimation of Parameters when the Observations are Subject to Measurement Error,"
Journal of the Graduate Research Center: Vol. 30:
1, Article 4.
Available at: https://scholar.smu.edu/journal_grc/vol30/iss1/4