The range inter-event process in a symmetric birth-death random walk

Pierre Vallois, Charles S. Tapiero

Research output: Contribution to journalArticlepeer-review


This paper provides new results for the range inter-events process of a birth-death random walk. Motivations for determining and using the inter-range event distribution have two sources. First, the analytical results we obtain are simpler than the range process and make it easier, therefore, to use statistics based on the inter-range event process. Further, most of the results for the range process are based on long-run statistical properties which limits their practical usefulness while inter-range events are by their nature 'short-term' statistics. Second, in many cases, data on amplitude change are easier to obtain and calculate than range and standard deviation processes. As a results, the predicted statistical properties of the inter-range event process can provide an analytical foundation for the development of statistical tests that may be used practically. Application to outlier detection, volatility and time-series analysis is discussed.

Original languageEnglish (US)
Pages (from-to)293-306
Number of pages14
JournalApplied Stochastic Models in Business and Industry
Issue number3
StatePublished - Jul 2001


  • Inter-range events process
  • R/S analysis
  • Range process

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Business, Management and Accounting
  • Management Science and Operations Research


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