Maximum likelihood estimation for a special exponential family under random double-truncation

Ya Hsuan Hu, Takeshi Emura*

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

17 Scopus citations


Doubly-truncated data often appear in lifetime data analysis, where samples are collected under certain time constraints. Nonparametric methods for doubly-truncated data have been studied well in the literature. Alternatively, this paper considers parametric inference when samples are subject to double-truncation. Efron and Petrosian (J Am Stat Assoc 94:824–834, 1999) proposed to fit a parametric family, called the special exponential family, with doubly-truncated data. However, non-trivial technical aspects, such as parameter space, support of the density, and computational algorithms, have not been discussed in the literature. This paper fills this gap by providing the technical aspects, including adequate choices of parameter space as well as support, and reliable computational algorithms. Simulations are conducted to verify the suggested techniques, and real data are used for illustration.

Original languageEnglish
Pages (from-to)1199-1229
Number of pages31
JournalComputational Statistics
Issue number4
StatePublished - 01 12 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.


  • Fixed point iteration
  • Newton–Raphson algorithm
  • Survival analysis
  • Truncated data


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