# Goodness-of-fit Test for the Weibull Distribution Based on Multiply Type-II Censored Samples

• Kang, Suk-Bok (Dept. of Statistics, Yeungnam Univ.) ;
• Han, Jun-Tae (Institute for National Health Insurance, National Health Insurance Co.)
• Published : 2009.03.30

#### Abstract

In this paper, we derive the approximate maximum likelihood estimators of the shape parameter and the scale parameter in a Weibull distribution under multiply Type-II censoring by the approximate maximum likelihood estimation method. We develop three modified empirical distribution function type tests for the Weibull distribution based on multiply Type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

#### References

1. Aho, M., Bain, L. J. and Engelhardt, M. (1985). Goodness-of-fit tests for the Weibull distribution with unknown parameters and heavy censoring, Journal of Statistical Computation and Simulation, 21, 213-225 https://doi.org/10.1080/00949658508810816
2. Balakrishnan, N., Gupta, S. S. and Panchapakesan, S. (1995). Estimation of the location and scale parameters of the extreme value distribution based on multiply Type-Ⅱ censored samples, Com-munications in Statistics-Theory and Methods, 24, 2105-2125 https://doi.org/10.1080/03610929508831605
3. Balakrishnan, N., Kannan, N., Lin, C. T. and Wu, S. J. S. (2004). Inference for the extreme value distribution under progressive Type-Ⅱ censoring, Journal of Statistical Computation and Simu-lation, 74, 25-45 https://doi.org/10.1080/0094965031000105881
4. Cho, Y. S., Lee, J. Y. and Kang, S. B. (1999). A study on distribution based on the transformed Lorenz curve, The Korean Journal of Applied Statistics, 12, 153-163
5. Gibson, E. W. B. and Higgins, J. J. (2000). Gap-ratio goodness of fit tests for Weibull or extreme value distribution assumptions with left or right censored data, Communications in Statistics-Simulation and Computation, 29, 541-557 https://doi.org/10.1080/03610910008813627
6. Han, J. T. and Kang, S. B. (2006), Estimation for two-parameter Rayleigh distribution based on multiply Type-Ⅱ censored sample, Journal of the Korean Data & Information Science Society, 17, 1319-1328
7. Kang, S. B. and Cho, Y. S. (2001). A study on distribution based on the normalized sample Lorenz curve, The Korean Communications in Statistics, 8. 185-192
8. Kang, S. B. and Lee, H. J. (2006a). Goodness-of-fit tests for the Weibull distribution based on the sample entropy, Journal of the Korean Data & Information Science Society, 17, 259-268
9. Kang, S. B. and Lee, S. K. (2006b). Test for the exponential distribution based on multiply Type-Ⅱ censored samples, The Korean Communications in Statistics, 13, 537-550 https://doi.org/10.5351/CKSS.2006.13.3.537
10. Lieblein, J. and Zelen, M. (1956). Statistical investigation of the fatigue life of deep-groove ball bearings, Journal of Research of the National Bureau of Standards, 57, 273-316 https://doi.org/10.6028/jres.057.033
11. Ng, H. K. T., Chan, P. S. and Balakrishnan, N. (2004). Optimal progressive censoring plan for the Weibull distribution, Technometrics, 46, 470-481 https://doi.org/10.1198/004017004000000482
12. Sanjel, D. and Balakrishnan, N. (2008). A Laguerre polynomial approximation for a goodness-of-fit test for exponential distribution based on progressively censored data, Journal of Statistical Computation and Simulation, 78, 503-513 https://doi.org/10.1080/00949650701216612
13. Wang, B. (2008). Goodness-of-fit test for the exponential distribution based on progressively Type-Ⅱ censored sample, Journal of Statistical Computation & Simulation, 78, 125-132 https://doi.org/10.1080/10629360600944266
14. Wu, J. W. and Yang, C. C. (2002). Weighted moments estimation of the scale parameter of the exponential distribution based on a multiply Type -Ⅱ censored sample, Quality and Reliability Engineering International, 18, 149-154 https://doi.org/10.1002/qre.456

#### Cited by

1. On the maximum likelihood estimators for parameters of a Weibull distribution under random censoring vol.23, pp.3, 2016, https://doi.org/10.5351/CSAM.2016.23.3.241
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.877467155456543, "perplexity": 3618.3788806848493}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178363217.42/warc/CC-MAIN-20210302034236-20210302064236-00117.warc.gz"}