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Censored lifespans in a double-truncated sample: Maximum likelihood inference for exponential and geometric distribution

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  • Sieg, Fiete
  • Toparkus, Anne-Marie
  • Weißbach, Rafael

Abstract

We approximate a small truncated sample of censored durations with a bivariate Poisson process. For exponential or geometric distribution of the duration, we derive the likelihood, profile out the unobservable sample size, and study identification, consistency as well as asymptotic normality.

Suggested Citation

  • Sieg, Fiete & Toparkus, Anne-Marie & Weißbach, Rafael, 2025. "Censored lifespans in a double-truncated sample: Maximum likelihood inference for exponential and geometric distribution," Statistics & Probability Letters, Elsevier, vol. 226(C).
    • Handle: RePEc:eee:stapro:v:226:y:2025:i:c:s016771522500149x
    DOI: 10.1016/j.spl.2025.110504
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    References listed on IDEAS

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    1. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    2. Takeshi Emura & Ya-Hsuan Hu & Yoshihiko Konno, 2017. "Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation," Statistical Papers, Springer, vol. 58(3), pages 877-909, September.
    3. Carla Moreira & Jacobo de Uña-Álvarez, 2010. "Bootstrapping the NPMLE for doubly truncated data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 567-583.
    4. Rafael Weißbach & Dominik Wied, 2022. "Truncating the exponential with a uniform distribution," Statistical Papers, Springer, vol. 63(4), pages 1247-1270, August.
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