Skip to main content

Non-parametric test for decreasing renewal dichotomous Markov noise shock model


Sepehrifar and Yarahmadian (Stat Pap 58:1115–1124, 2017) had developed a non-parametric test for testing exponentiality against decreasing renewal dichotomous Markov noise shock model (DRDMNS) alternatives which when subjected to scrutiny under delivers. Hence, we propose a non-parametric test for testing exponentiality against a class of distributions belonging to DRDMNS models. The asymptotic properties of the test statistic are discussed. An exact null distribution is derived and critical values with different sample sizes are obtained. The proposed test is applied to the censored data also. The results of the Monte Carlo simulations are used to further manifest the quality of the proposed test. Finally, the proposed test is illustrated using two real data sets.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4


  1. Abouammoh AM, Abdulghani SA, Qamber IS (1994) On partial ordering and testing of new better than renewal used classes. Reliab Eng Syst Saf 43:37–41

    Article  Google Scholar 

  2. Ahmad IA, Mugdadi AR (2009) Higher order equilibrium life distributions. IEEE Trans Reliab 59:66–73

    Article  Google Scholar 

  3. Bena I (2006) Dichotomous Markov noise: exact results for out-of-equilibrium systems. Int Modern Phys B 20:2825–2888

    MathSciNet  Article  Google Scholar 

  4. Bicout DJ (1997) Greens functions and first passage time distributions for dynamic instability of microtubules. Phys Rev J 5:6656–6667

    Google Scholar 

  5. Box GEP (1954) Some theorems on quadratic forms applied in the study of analysis of variance problems, I. Effect of inequality of variance in the one-way classification. Ann Math Stat 25:290–302

    MathSciNet  Article  Google Scholar 

  6. Datta S, Bandyopadhyay D, Satten GA (2010) Inverse probability of censoring weighted U-statistics for right-censored data with an application to testing hypotheses. Scand J Stat 37:680–700

    MathSciNet  Article  Google Scholar 

  7. Harandi FM, Yarahmadian S, Sepehrifar M, van Gelder PHAJM (2014) The dichotomous Markov process with nonparametric test application: a decision support method in long-term river behavioural analysis: the Zayandeh Rud River; a case study from central Iran. Stoch Env Res Risk Assess 28:1889–1896

    Article  Google Scholar 

  8. Koul HL, Susarla V (1980) Testing for new better than used in expectation with incomplete data. J Am Stat Assoc 75:952–956

    MathSciNet  Article  Google Scholar 

  9. Lee AJ (1990) U-Statistics. Marcel Dekker Inc., New York

    MATH  Google Scholar 

  10. Proschan F (1963) Theoretical explanation of observed decreasing failure rate. Technometrics 5:375–383

    MathSciNet  Article  Google Scholar 

  11. Sepehrifar M, Yarhmadian S (2017a) Decreasing renewal dichotomous Markov noise shock model with hypothesis testing applications. Stat Pap 58:1115–1124

    MathSciNet  Article  Google Scholar 

  12. Sepehrifar M, Yarahmadian S (2017b) Testing monotonic equilibrium residual entropy of N-state random evolution. Commun Stat Theory Methods 46:10088–10096

    MathSciNet  Article  Google Scholar 

  13. Zhao H, Tsiatis AA (2000) Estimating mean quality adjusted lifetime with censored data. Sankhya-B 62:175–188

    MathSciNet  MATH  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Sudheesh K. Kattumannil.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mohan, R., N, S. & Kattumannil, S.K. Non-parametric test for decreasing renewal dichotomous Markov noise shock model. Stat Papers (2021).

Download citation


  • Dichotomous Markov noise model
  • Right censoring
  • U-statistics