Abstract
We first give historical remarks about the forgotten univariate Teissier model. We introduce symmetric and asymmetric bivarite versions of the Teissier distribution and outline basic properties. The corresponding copula is obtained and applications are discussed.
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References
Teissier, G.: Recherches sur le vieillissement et sur les lois de mortalite. Annales de Physiologie et de Physicochimie Biologique 10, 237–284 (1934)
Swartz, B.: The mean residual lifetime function. IEEE Trans. Reliab. 32, 108–109 (1973)
Gompertz, B.: On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos. Trans. Royal Soc. Lond. 115, 513–583 (1825)
Laurent, A.G.: Failure and mortality from wear and ageing. The teissier model. In: Patil, G.P., Kotz, S., Ord, J.K. (eds.) A Modern Course on Statistical Distributions in Scientific Work. ASIC, vol. 17, pp. 301–320. Springer, Heidelberg (1975). https://doi.org/10.1007/978-94-010-1845-6_22
Rinne, H.: Estimating the lifetime distribution of private motor-cars using prices of used cars: the teissier model. In: Statistiks Zwischen Theorie und Praxis, pp. 172–184 (1981)
Muth, J.: Reliability models with positive memory derived from the mean residual life function. Theor. Appl. Reliab. 2, 401–435 (1977)
Leemis, L., McQueston, J.: Univariate distribution relationships. Am. Stat. 62, 45–53 (2008)
Jodra, P., Jimenez-Gamero, M., Alba-Fernandez, M.: On the Muth distribution. Math. Model. Anal. 20, 291–310 (2015)
Corless, R.M., Gonnet, G.H., Hare, D.E., Jeffrey, D.J., Knuth, D.E.: On the LambertW function. Adv. Comput. Math. 5(1), 329–359 (1996)
Arnold, B.C., Zahedi, H.: On multivariate mean remaining life functions. J. Multivar. Anal. 25(1), 1–9 (1988)
Kulkarni, H., Rattihalli, R.: Characterization of bivariate mean residual-life function. IEEE Trans. Reliab. 45(2), 249–253 (1996)
Sankaran, P., Sreeja, V.: Proportional hazards model for multivariate failure time data. Commun. Stat. Theor. Methods 36, 1627–1642 (2007)
Joe, H.: Dependence Modeling with Copulas. Monographs on Statistics and Applied Probability, vol. 134. CRC Press, Boca Raton (2015)
Acknowledgments
The first named author is partially supported by FAPESP Grant 2013/07375-0 and the third named author is supported by CNPq grant provided by USP. We are thankful to Daniel de Brito Reis who designed the Figures.
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Kolev, N., Ngoc, N., Ju, Y.T. (2017). Bivariate Teissier Distributions. In: Rykov, V., Singpurwalla, N., Zubkov, A. (eds) Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science(), vol 10684. Springer, Cham. https://doi.org/10.1007/978-3-319-71504-9_24
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DOI: https://doi.org/10.1007/978-3-319-71504-9_24
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