"Degenerate and poisson convergence criteria for success runs" by Anant P. Godbole
 

Degenerate and poisson convergence criteria for success runs

Document Type

Article

Publication Date

8-1990

Department

Department of Mathematical Sciences

Abstract

Let N(k)n be the number of success runs of length k > 1 in n Bernoulli trials, each with success probability pn. We show that N(k)n converges weakly to the distribution degenerate at zero as n → ∞, nf(pn) → λ (0 < λ < ∞) for any ∝ satisfying pkn = o(∝(pn)) (n → ∞). This answers, in the negative, a question posed by Philippou and Makri (1986) who suspected that a Poisson distribution of order k might be the target limit (if ∝(pn) = pn). If, instead, npkn → λ, we prove that N(k)n tends in law to a Poisson(λ) random variable. This improves a classical result of von Mises (1921) which required, in addition, that k → ∞. Rates of convergence are provided for the above results.

Publication Title

Statistics and Probability Letters

Plum Print visual indicator of research metrics
PlumX Metrics
  • Citations
    • Citation Indexes: 12
  • Usage
    • Abstract Views: 5
  • Captures
    • Readers: 1
see details

Share

COinS