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The MLE of the uniform distribution with right-censored data

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  • Qiqing Yu

    (SUNY)

Abstract

We carry out parametric inferences to a breast cancer data set which is right censored using the uniform distribution U(a, b). Under right censoring, it is rare that one can find the explicit solution to the maximum likelihood estimator (MLE) under the parametric set-up, except for the exponential distribution $$Exp(\theta )$$ E x p ( θ ) . We show that the MLE of a has a closed form solution, whereas the MLE of b has a closed form solution in some sense. We further propose a diagnostic plotting method and test for U(a, b). The asymptotic properties of the MLE are also investigated. It turns out that this breast cancer data set fits both U(a, b) and $$Exp(\theta )$$ E x p ( θ ) . Moreover, U(a, b) leads to more useful and reasonable inferences than those using the product-limit estimator or using the MLE of $$Exp(\theta )$$ E x p ( θ ) .

Suggested Citation

  • Qiqing Yu, 2021. "The MLE of the uniform distribution with right-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 662-678, October.
    • Handle: RePEc:spr:lifeda:v:27:y:2021:i:4:d:10.1007_s10985-021-09528-2
    DOI: 10.1007/s10985-021-09528-2
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    References listed on IDEAS

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    1. Julian Górny & Erhard Cramer, 2019. "Type-I hybrid censoring of uniformly distributed lifetimes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(2), pages 412-433, January.
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