The Lorenz curve for model assessment in exponential order statistic models

Jason A. Osborne*, Thomas A. Severini

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review


A goodness-of-fit technique for random samples from the exponential distribution based on the sample Lorenz curve is adapted for use in the exponential order statistic (EOS) model. In the EOS model, only those observations in a random sample from the exponential distribution of unknown size N that are less than some known stopping time T are observable. The model is known as the Jelinski-Moranda model in software reliability, where it is used to estimate the number of bugs in software during development. Distributional results are derived for the distance between the sample Lorenz curve and the population Lorenz curve so that it can be used as a goodness-of-fit test statistic. Simulations show that the test has good power against several alternative distributions. Simulations also indicate that in some cases, model misspecification leads to poor parameter estimation, A plotting procedure provides a means of graphical assessment of fit.

Original languageEnglish (US)
Pages (from-to)87-97
Number of pages11
JournalJournal of Statistical Computation and Simulation
Issue number1
StatePublished - 2002


  • Conditional probability integral transform
  • Goodness-of-fit
  • Kolmogorov-Smirnov distance
  • Lorenz curve
  • Software reliability

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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