The Lorenz and the Scaled Total-Time-on-Test Transform Curves: A Unified Approach

IEEE Transactions on Reliability

Volumn 43, Issue 1, 1994, Pages 76-84

  Pham, T G ^a   Turkkan, N ^a  

^a UNIVERSITÉ DE MONCTON   (Canada)

Author keywords

curve; Gamma distribution; Gini index; Lorenz curve; Pietra ratio; Scaled total time on test transform

Indexed keywords

COMPUTER SOFTWARE; CURVE FITTING; DATA REDUCTION; ECONOMICS; GRAPHIC METHODS; PROBABILITY; STATISTICAL METHODS; STATISTICAL TESTS;

GAMMA DISTRIBUTION; GINI INDEX; LORENZ CURVE; PIETRA RATIO; SCALED TOTAL TIME ON TEST TRANSFORM CURVE;

RELIABILITY THEORY;

EID: 0028385071     PISSN: 00189529     EISSN: 15581721     Source Type: Journal    
DOI: 10.1109/24.285115     Document Type: Article

References (19)

1. M. V. Aarset, “How to identify a bathtub hazard rate”, IEEE Trans. Reliability, vol R-36, 1987 Apr, pp 106–108.
2. J.I. Ansell, M.J. Phillips, “Practical problems in the statistical analysis of reliability data”, Applied Statistics, JRSS/C, vol 38, 1989 Apr, pp 205–247.
3. B.C. Arnold, “Majorization and the Lorenz order: A brief introduction”, Lecture Notes in Statistics, no 43, 1987; Springer Verlag.
4. R.E. Barlow, “Geometry of the total time on test transform”, Naval Research Logistics Quarterly, vol 26, 1979, pp 393–402.
5. R.E. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, 1975; Holt, Rinehart, Winston.
6. J.A. Bishop, J.P. Formby, W.J. Smith, “Lorenz dominance and welfare: Changes in the US distribution of income 1967-1986”, Review of Economics & Statistics, 1991 May, pp 134–139.
7. M. Chandra, N.K. Singpurwalla, “Relations between some notions which are common to reliability theory and economics”, Mathematics of Operations Research, 1981, pp 113–121.
8. C. Dagum, “Lorenz curve”, Encyclopedia of Statistics (Johnson & Kotz, Eds), vol 5, 1981, pp 157–161.
9. J.L. Gastwirth, “The estimation of the Lorenz curve and Gini index”, Review Economics & Statistics, vol 54, 1972 Sep, pp 306–316.
10. J.L. Gastwirth, “Large sample theory of some measures of income inequality”, Econometrica, vol 42, 1974 Jan, pp 191–196.
11. B. Klefsjö, “Reliability interpretations of some concepts from economics”, Naval Research Logistics Quarterly, vol 31, 1984, pp 301–308.
12. B. Klefsjö, “T-T-T- plotting - A tool for both theoretical and practical problems”, J. Statistical Planning & Inference, vol 29, 1991, pp 99–110.
13. J.B. McDonald & B.C. Jensen, “An analysis of some properties of alternative measures of income inequality based on the Gamma distribution function”, J. Amer. Statistical Assoc, vol 74, 1979 Dec, pp 856–860.
14. T. Pham, N. Turkkan, “Determination of the beta distribution from its Lorenz curve”, Math. & Computer Modelling J., vol 16, 1992, pp 73–84.
15. T. Pham, N. Turkkan, “Using the mean deviation in determining the prior distribution”, Stat. & Prob. Letters, vol 13, 1992 Apr, pp 373–381.
16. T. Pham, N. Turkkan, “The hazard rate ordering of distributions”, Statistics & Probability Letters, 1994 Sep (scheduled to appear).
17. S. Ross, Stochastic Processes, 1983; John Wiley & Sons.
18. P.K. Sen, “The Gini coefficient and poverty indexes: Some reconciliations”, J. Amer. Statistical Assoc, vol 81, 1986 Dec, pp 1050–1057.
19. M. Shaked, “Dispersive ordering of distributions”, J. Applied Probability, vol 19, 1982, pp 310–320.