A Family of Tests for Trend Change in Mean Residual Life with Known Change Point

  • Na, Myung-Hwan (Department of Naval Architecture and Ocean Engineering, Chosun University) ;
  • Kim, Jae-Joo (Department of Statistics, Seoul National University)
  • Published : 2000.12.01


The mean residual function is the expected remaining life of an item at age x. The problem of trend change in the mean residual life is great interest in the reliability and survival analysis. In this paper, we develop a family of test statistics for testing whether or not the mean residual life changes its trend. The asymptotic normality of the test statistics is established. Monte Carlo simulations are conducted to study the performance of our test statistics.


  1. Scandinavian Journal of Statistics v.17 no.3 Tests for Monotonicity Properties of the Mean Residual Life Function Aly, E.E.A.A.
  2. SIAM Journal of Algebraic Discrete Methods v.3 The Class of Mean Residual Lives and Some Consequences Bhattacharjee, M.C.
  3. Annals of Statistics v.8 A Note on Differentials and the CLT and LIL for Statistical Functions, with Application ti M-Estimates Boos, D.D.;Serfling, R.J.
  4. Renewal Theory Cox, D.R.
  5. Annals of Statistics v.14 Testing Exponentiality versus a Trend Change in Mean Residual Life Guess, F.;Hollander, M.;Proschan, F.
  6. Handbook of Statistics : Quality Control and Reliability v.7 Mean Residual Life : Theory and Application Guess, F.;Proschan, F.
  7. Annals of Statistics v.20 Testing exponentiality against IDMRL Distributions with Unknown Change Point Hawkins, D.L.;Kochar, S.;Loader, C.
  8. Statistics and Related Topics Mean Residual Life Hall, W.;Wellner, J.A.
  9. Advance in Applied Probability v.12 Some new Approaches to Probability Distribution Kotz, S.;Shanbhang, D.N.
  10. IEEE Transacation on Reliability v.44 no.2 Trend Change in Mean Residual Life Lim, J.H.;Park, D.H.
  11. Communication in Statistics - Theory and Methods v.27 no.5 A Family of Tests for Trend Change in Mean Residual Life Lim, J.H.;Park, D.H.
  12. Journal of the Korean Society for Quality Management v.26 no.4 A Study on the Test for Tren Change in Mean Residual Life Na, M.H.;Lee, H.W.;Kim, J.J.
  13. Approximation Theorems of Mathematical Statistics Serfling, R.J.
  14. Annals of Mathematical Statistics v.18 On the Asymptotic Distribution of Differectiable Statistical Functions von Mises, R.