- Volume 9 Issue 3
Shapiro and Wilk(1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test based on the statistic is inconsistent Kim(2001a) proposed a modified Shapiro-Wilk's test statistic using the ratio of two asymptotically efficient estimators of scale. In this paper, we study the consistency of the proposed test.
exponentiality;goodness of fit tests;consistency;order statistics
- Probability and Mathematical Statistics Chung, K. L.
- Empirical processes with applications to statistics Shorack, G. R.;Wellner, J. A.
- Goodness-of-fit Techniques D'Agostino, R. B.;Stephens, M. A.
- South African Statistical Journal v.7 A goodness of fit test for a scale parameter family of distributions de Wet, T.;Venter, J. H.
- The Korean Communications in Statistics v.8 A modification of the W test for exponentiality Kim, N.
- The Korean Communications in Statistics v.8 The limit distribution of a modified W-test statistics for exponentiality Kim, N.
- Technometrics v.29 Tests for exponentiality when origin and scale parameters are unknown Spinelli, J. J.;Stephens, M. A. https://doi.org/10.2307/1269459
- Technometrics v.14 An analysis of variance test for the exponential distribution (complete samples) Shapiro, S. S.;Wilk, M. B. https://doi.org/10.2307/1267427
- Annals of Mathematical Statistics v.40 Linear functions of order statistics Stigler, S. M. https://doi.org/10.1214/aoms/1177697587
- Annals of Mathematical Statistics v.38 Asymptotic distribution of linear combinations of functions of order statistics with applications to estimation Chernoff, H.;Gastwirth, J. L.;Johns, M. V. https://doi.org/10.1214/aoms/1177699058
- Probability and measure Billingsley, P.
- The Shapiro-Wilk Type Test for Exponentiality Based on Progressively Type II Censored Data vol.23, pp.3, 2010, https://doi.org/10.5351/KJAS.2010.23.3.487