×

Information measures in biostatistics and reliability engineering. (English) Zbl 1404.92012

Rykov, Vladimir V. (ed.) et al., Mathematical and statistical models and methods in reliability. Applications to medicine, finance, and quality control. Invited papers based on the presentation at the 6th international conference (MMR 2009), Moscow, Russia, June 22–26, 2009. Boston, MA: Birkhäuser (ISBN 978-0-8176-4970-8/hbk; 978-0-8176-4971-5/ebook). Statistics for Industry and Technology, 401-413 (2010).
Summary: In this paper, we discuss the basic tools for modelling in Biomedicine and Reliability. In particular, we present the divergence measures and the tests of fit while optimal modelling issues are also addressed. The last section is devoted to various applications in Reliability, Biomedicine, Hydrology, and Insurance and Actuarial Science.
For the entire collection see [Zbl 1203.60007].

MSC:

92B15 General biostatistics
62P10 Applications of statistics to biology and medical sciences; meta analysis
62N05 Reliability and life testing
Full Text: DOI

References:

[1] Aguirre, N., Nikulin, M.: Chi-squared goodness-of-fit test for the family of logistic distributions. Kybernetika, 30, 214-222 (1994) · Zbl 0827.62017
[2] Akaike, H.: Information theory and an extension of the maximum likelihood principle. In: Petrov B. N. and Csaki F. (eds) Proceedings of the 2nd International Symposium on Information Theory, Akademiai Kaido, Budapest (1973) · Zbl 0283.62006
[3] Ali, S. M., Silvey, S. D.: A general class of coefficients of divergence of one distribution from another. J. Roy. Statist. Soc. B, 28, 131-142 (1966) · Zbl 0203.19902
[4] Bagdonavi\(\(\check{\text{c}}\)\)ius, V., Nikulin, M. S.: Goodness-of-fit tests for accelerated life models. In: Huber-Carol, C., Balakrishnan, N., Nikulin, M. S., and Mesbah, M. (eds) Goodness-of-fit tests and Model Validity, Birkhauser, Boston, 281-297 (2002) · Zbl 1127.62410
[5] Basu, A., Harris, I. R., Hjort, N. L., Jones, M. C.: Robust and efficient estimation by minimising a density power divergence. Biometrika, 85, 549-559 (1998) · Zbl 0926.62021 · doi:10.1093/biomet/85.3.549
[6] Cavanaugh, J. E.: Criteria for linear model selection based on Kullback’s symmetric divergence. Aust. N. Z. J. Stat., 46, 257-274 (2004) · Zbl 1061.62004 · doi:10.1111/j.1467-842X.2004.00328.x
[7] Chen, H. S., Lai, K., Ying, Z.: Goodness-of-fit tests and minimum power divergence estimators for survival data. Stat. Sin., 14, 231-248 (2004) · Zbl 1035.62100
[8] Chhikara, R. S., Folks, J. L.: The inverse Gaussian distribution as a lifetime model. Technometrics, 19, 461-468 (1977) · Zbl 0372.62076 · doi:10.1080/00401706.1977.10489586
[9] Clayton, D., Cuzick, J.: Multivariate generalizations of the proportional hazards model (with discussion). J. Roy. Stat. Soc., A 148, 82-117 (1985) · Zbl 0581.62086
[10] Clayton, D., Cuzick, J.: The semiparametric Pareto model for regression analysis of survival times. Papers on Semiparametric Models MS-R8614, Centrum voor Wiskunde en Informatica, Amsterdam, 19-31 (1986)
[11] Cressie, N., Read, T. R. C.: Multinomial goodness-of-fit tests, JRSSB, 5, 440-454 (1984) · Zbl 0571.62017
[12] Csiszar, I.: Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Bewis der Ergodizitat on Markhoffschen Ketten. Publication of the Mathematical Institute of the Hungarian Academy of Sciences, 8, 84-108 (1963)
[13] Di Crescenzo, A., Longobardi, M.: A measure of discrimination between past lifetime distributions. Stat. Probab. Lett., 67, 173-182 (2004) · Zbl 1058.62088 · doi:10.1016/j.spl.2003.11.019
[14] Ebrahimi, N., Kirmani, S. N. U. A.: A measure of discrimination between two residual life-time distributions and its applications. Ann. Inst. Stat. Math., 48, 257-265 (1996) · Zbl 0861.62063 · doi:10.1007/BF00054789
[15] Folks, J. L., Chhikara, R. S.: The inverse Gaussian distribution and its statistical application - a review. J. Roy. Stat. Soc. B, 40, 263-289 (1978) · Zbl 0408.62011
[16] Gacula Jr., M. C., Kubala, J. J.: Statistical models for shelf life failures. J. Food Sci., 40, 404-409 (1975) · doi:10.1111/j.1365-2621.1975.tb02212.x
[17] Huber-Carol, C., Vonta, F.: Frailty models for arbitrarily censored and truncated data. Lifetime Data Anal., 10(4), 369-388 (2004) · Zbl 1058.62102 · doi:10.1007/s10985-004-4773-y
[18] Huberman, B. A., Pirolli, P. L. T., Pitkow, J. E., Lukose, R. M.: Strong regularities in world wide web surfing. Science, 280, 95-97 (1998) · doi:10.1126/science.280.5360.95
[19] Kullback, S., Leibler, R.: On information and sufficiency. Ann. Math. Stat., 22, 79-86 (1951) · Zbl 0042.38403 · doi:10.1214/aoms/1177729694
[20] Marsh, P.: Data driven likelihood ratio tests for goodness-to-fit with estimated parameters. Discussion Papers in Economics, Department of Economics and Related Studies, The University of York, 2006/20 (2006)
[21] Mattheou, K., Karagrigoriou, A.: A new family of divergence measures for tests of fit. Aust. N. Z. J. Stat. 52, 187-200 (2010) · Zbl 1337.62012 · doi:10.1111/j.1467-842X.2010.00574.x
[22] Mattheou, K., Lee, S., Karagrigoriou, A.: A model selection criterion based on the BHHJ measure of divergence. J. Stat. Plan. Infer., 139, 128-135 (2009) · Zbl 1149.62002 · doi:10.1016/j.jspi.2008.04.022
[23] Menéndez, M. L., Pardo, J. A., Pardo, L., Pardo, M. C.: Asymptotic approximations for the distributions of the \(h\), ϕ-divergence goodness-of-fit statistics: applications to Rényi’s statistic. Kybernetes, 26, 442-452 (1997) · Zbl 1067.62513 · doi:10.1108/03684929710176449
[24] Moghadam, M., Eskandari, F.: Quality improvement by using inverse Gaussian model in robust engineering. Qual. Quantity, 40, 157-174 (2006) · doi:10.1007/s11135-005-8082-7
[25] O’Reilly, F.J., Rueda, R.: Goodness of fit for the inverse Gaussian distribution. Can. J. Stat., 20, 387-397 (1992) · Zbl 0765.62051 · doi:10.2307/3315609
[26] Pardo, L.: Statistical Inference Based on Divergence Measures. Chapman and Hall/CRC, London (2006) · Zbl 1118.62008
[27] Read, T. R. C.: Closer asymptotic approximations for the distributions of the power divergence goodness-of-fit statistics. Ann. Inst. Stat. Math., 36, 59-69 (1984) · Zbl 0554.62015 · doi:10.1007/BF02481953
[28] Read, T. R. C., Cressie, N.: Goodness-of-Fit Statistics for Discrete Multivariate Data. Springer Verlag, New York (1988) · Zbl 0663.62065 · doi:10.1007/978-1-4612-4578-0
[29] Sim, C. H.: Inverse Gaussian control charts for monitoring process variability. Commun. Stat., Simul. Comput., 32, 223-239 (2003) · Zbl 1100.62527
[30] Siotani, M., Fujikoshi, Y.: Asymptotic approximations for the distributions of multinomial goodness-of-fit statistics. Hiroshima Math. J. 14, 115-124 (1984) · Zbl 0553.62017
[31] Tremblay, L.: Using the Poisson inverse Gaussian in Bonus-Malus systems. ASTIN Bulletin International Actuarial Association, 22:1, 97-106, http://www.casact.org/library/astin/vol22no1/97.pdf (1992)
[32] Vaupel, J. W., Manton, K. G., Stallard, E.: The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, 439-454 (1979) · doi:10.2307/2061224
[33] Vonta, F., Artemiou, A.: Hypothesis testing in frailty models for arbitrarily censored and truncated data. Comm. Dependability Qual. Man. 10(1), 110-121 (2007)
[34] Vonta, F., Karagrigoriou, A.: Generalized measures of divergence in survival analysis and reliability. J. Appl. Probab., 47(1), 216-234 (2010) · Zbl 1185.62012 · doi:10.1239/jap/1269610827
[35] Yanagihara, H., Tonda, T., Matsumoto, C.: Bias correction of cross-validation criterion based on the Kullback-Leibler information under a general condition. J. Multivariate Anal. 97, 1965-1975 (2006) · Zbl 1101.62047 · doi:10.1016/j.jmva.2005.10.009
[36] Yarnold, J. K.: Asymptotic approximations for the probability that a sum of lattice random vectors lies in a convex set. Ann. Math. Stat., 43, 1566-1580 (1972) · Zbl 0256.62022 · doi:10.1214/aoms/1177692389
[37] Zhang, J.: Powerful goddness-of-fit tests based on likelihood ratio. J. R. Stat. Soc. Ser. B, 64(2), 281-294 (2002) · Zbl 1067.62046 · doi:10.1111/1467-9868.00337
[38] Zografos, K., Ferentinos, K., Papaioannou, T.: \(Φ\)-divergence statistics: sampling properties, multinomial goodness of fit and divergence tests. Comm. Statist. Theor. Meth., 19(5), 1785-1802 (1990) · Zbl 0724.62007 · doi:10.1080/03610929008830290
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.