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Estimating a survival curve when new is better than used in expectation

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  • Lyn R. Whitaker
  • Francisco J. Samaniego

Abstract

Let X be a positive random variable. The distribution F of X is said to be “new better than used in expectation,” or “NBUE,” if E(X) ⩾ E(X – t|X > t) for all t ⩾ 0. Suppose X1, …, Xn, is a random sample from an NBUE distribution F. The problem of estimating F by a distribution which is itself NBUE is considered. The estimator Gn, defined as the NBUE distribution supported on the sample which minimizes the (sup norm) distance between the NBUE class and the empirical distribution function, is studied. The strong uniform consistency of Gn, is proven, and a numerical algorithm for obtaining Gn, is given. Our approach is applied to provide an estimate of the distribution of lifetime following the diagnosis of chronic granulocytic leukemia based on data from a National Cancer Institute study.

Suggested Citation

  • Lyn R. Whitaker & Francisco J. Samaniego, 1989. "Estimating a survival curve when new is better than used in expectation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 693-707, October.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:5:p:693-707
    DOI: 10.1002/1520-6750(198910)36:53.0.CO;2-F
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    Cited by:

    1. Lorenzo, Edgardo & Malla, Ganesh & Mukerjee, Hari, 2013. "Estimation of distributions with the new better than used in expectation property," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1346-1352.

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