Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지

Test for Trend Change in NBUE-ness Using Randomly Censored Data

  • Dae-Kyung Kim (Department of Statistics, Dongguk University, Seoul 100-715) ;
  • Dong-Ho Park (Department of Statistics, Hallym University, Chunchon, 200-702) ;
  • June-Kyun Yum (Department of Statistics, Dongguk University, Seoul, 100-715)
  • Published : 1995.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

Let F be a life distribution with finite mean $\mu$ Then F is said to be in new better then worse than used in expectation (NBWUE(p)) class if $\varphi(u) {\geq} u$ for $0 {\leq}u{\leq}t_0$ and ${\varphi}(u) {\leq} u$ for $t_0< u {\leq} 1$ where ${\varphi}(u)$ is the scaled total-time-on-test transform and $p=F(t_0)$. We propose a testing procedure for $H_0$ : F is exponential against $H_1$ : NBWUE(p), and is not expontial, (or $H_1\;'$ : F is NWBUE (p), and is not exponential) using randomly censored data. Our procedure assumes kmowledge of the proportion p of the population that fail at or before the change-point $\t_0$. Know ledge of $\t_0$ itself is not assumed. The asymptotic normality of the test statistic is established and a Monte Carlo experiment is performed to investigate the speed of convergence of the test statistic to normality. The power of our test is also studied.

Keywords

References

  1. Annals of Statistics v.2 Large sample behavior of the product-limit estimator on the whole line Gill,R.D.
  2. Ph. D. dissertation Testing whether mean residual life changes trends Guess,F.
  3. Annals of Statistics v.14 Testing exponentialilty versus a trend change in mean residual life Guess,F.;Hollander,M.;Proschan,F
  4. Ph. D. dissertation A study on inference for a change point in failure rates Jeong,H.S.
  5. Technical Report, M613 Asymptotic normality of L-statistics with randomly censored data Joe,H.;Proschan,F.
  6. Technical Report, M613 Testing against a change in the NBUE-property Klefsjo,B
  7. Journal of American Statistical Association v.53 Nonparametric estimation from incomplete observations Kaplan,E.L.;Meier,P.
  8. Annals Statistics v.13 Asymptotic score-statistic process and tests for a constant hazard against a change-point alternative Mattews,D.E.;Farewell,V.T.;Pyke,R.
  9. Journal of Statistical Planning and Inference v.39 On nonparametric family of life distribution and its dual Mitra,M.;Basu,S.K.
  10. IEEE Transactions on Reliability v.37 Testing whether failure rate changes its trend Park,D.H.