### Abstract

Navarro and Ruiz [1] express the nonparametric maximum likelihood estimator (NPMLE) of the distribution of a failure-time random variable as a function of the NPMLE of generalized failure-rate functions. These generalized failure-rate functions are equal to the probability density functions of a doubly-truncated failure-time random variable at the endpoints of the truncating interval. Readers can infer from this paper that this simple estimator can be applied to a doubly-truncated sample of failure times. This commentary explains why that estimator does not apply to the general setting in which the observed failure times are doubly-truncated with subject-specific truncating intervals. A doubly-truncated sample of times to brain tumor progression illustrates the deviation of that estimator [1] from the NPMLE for these data. Definitions Quasar: unusually luminous objects found in remote areas of the universe; stellar object: nonquasar object; redshift: the shift in an object'S spectral lines toward the red end, indicating how fast the object is moving away from the observer.

Original language | English (US) |
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Pages (from-to) | 7-8 |

Number of pages | 2 |

Journal | IEEE Transactions on Reliability |

Volume | 52 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2003 |

### Keywords

- Double truncation
- Nonparametric maximum likelihood

### ASJC Scopus subject areas

- Safety, Risk, Reliability and Quality
- Electrical and Electronic Engineering

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## Cite this

*IEEE Transactions on Reliability*,

*52*(1), 7-8. https://doi.org/10.1109/TR.2002.807241