Skip to main content
SpringerLink
Log in

Some strong ε-equivalence of random variables

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

Strongness and related error evaluations are investigated on type (B)d, type (A) and type (I) ε-equivalence of random variables, which are based on Kolmogorov-Smirnov distance, a difference of random variables and Kullback-Leibler information number, respectively. As an application the Prohorov-LeCam type binomial-Poisson approximation problem is discussed and is given the best possible constant for the problem. Similar discussions are made on the negative binomial-Poisson approximation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Church, J. D. and Harris, B. (1970). The estimation of reliability from stress-strength relationships,Technometrics,12, 49–54.

    Article  Google Scholar 

  2. Hodges, J. L., Jr. and LeCam, L. (1960). The Poisson approximation to the Poisson binomial distribution,Ann. Math. Statist.,31, 737–740.

    Article  MathSciNet  Google Scholar 

  3. Ikeda, S. (1963). Asymptotic equivalence of probability distributions with applications to some problems of asymptotic independence,Ann. Inst. Statist. Math.,15, 87–116.

    Article  MathSciNet  Google Scholar 

  4. Ikeda, S. (1969). A remark on the incomparability of two criteria for a uniform convergence of probability measures,Ann. Inst. Statist. Math.,21, 533–536.

    Article  Google Scholar 

  5. Kerstan, J. (1964). Verallgemeinerung eines Satzes von Prochorow und LeCam,Zeit. Wahrscheinlichkeitsth.,2, 173–179.

    Article  Google Scholar 

  6. Kraft, O. and Schmitz, N. (1969). A note on Hoeffding's inequality,J. Amer. Statist. Ass.,64, 907–912.

    Article  MathSciNet  Google Scholar 

  7. LeCam, L. (1965). On the distribution of sums of independent random variables, “Bernoulli, Bays, Laplace”, proceedings of an international research seminar (Berkeley 1963), Springer, Berlin, 179–202.

    Google Scholar 

  8. Matsunawa, T. (1975). On the error evaluation of the joint normal approximation for sample quantiles,Ann. Inst. Statist. Math.,27, 189–199.

    Article  MathSciNet  Google Scholar 

  9. Matsunawa, T. (1976). Some inequalities based on inverse factorial series,Ann. Inst. Statist. Math.,28, A, 291–305.

    Article  MathSciNet  Google Scholar 

  10. Matsunawa, T. (1977). Approximations to the probabilities of binomial and multinomial random variables and chi-squarety pe statistics,Ann. Inst. Statist. Math.,29, A, 333–358.

    Article  MathSciNet  Google Scholar 

  11. Matsunawa, T. (1982). Uniform ϕ-equivalence of probability distributions based on information and related measures of discrepancy,Ann. Inst. Statist. Math.,34, A, 1–17.

    Article  MathSciNet  Google Scholar 

  12. Meshalkin, L. D. (1968). On the robustness of some characterizations of the normal distribution,Ann. Math. Statist.,39, 1747–1750.

    Article  MathSciNet  Google Scholar 

  13. Prohorov, Yu. V. (1953). Asymptotic behavior of the binomial distribution,Uspehi Matematicheskiikh Nauk,8, 135–142.

    MathSciNet  Google Scholar 

  14. Romanovska, M. (1977). A note on the upper bound for the distance in total variation between the binomial and the Poisson distribution,Statist. Neerlandica,31, 127–130.

    Article  Google Scholar 

  15. Vervaat, W. (1969). Upper bounds for the distance in total variation between the binomial or negative binomial and the Poisson distribution,Statist. Neerlandica,23, 79–86.

    Article  MathSciNet  Google Scholar 

Download references

Authors
  1. T. Matsunawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The Institute of Statistical Mathematics

About this article

Cite this article

Matsunawa, T. Some strong ε-equivalence of random variables. Ann Inst Stat Math 34, 209–224 (1982). https://doi.org/10.1007/BF02481023

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02481023

Keywords

Search

Navigation