Statistical inference for a general class of distributions with time-varying parameters

References

• C.W. Ahn, K.C. Chae, and G.M. Clark, Estimating parameters of the power law process with two measures of failure time, J. Qual. Technol. 30 (1998), pp. 127–132. doi: 10.1080/00224065.1998.11979831
   Web of Science ®Google Scholar
• H. Akaike, Information theory and an extension of the maximum likelihood principle. In 2nd International Symposium on Information Theory, B.N. Petrov, F. Csaki, eds., Akademia Kiado, Budapest, 1973, pp. 267–281,
   Google Scholar
• N. Balakrishnan and M. Stehlík, Likelihood testing with censored and missing duration data, J. Stat. Theory. Pract. 9 (2014), pp. 2–22. doi: 10.1080/15598608.2014.927811
   Google Scholar
• K. Balasubramanian, M.I. Beg, and R.B. Bapat, On families of distributions closed under extrema, Sankhya Indian J. Stat. A 53 (1991), pp. 375–388.
   Google Scholar
• V.S. Barbu, A. Karagrigoriou, and A. Makrides, Semi-Markov modelling for multi-state systems, Methodol. Comput. Appl. Probab. 19 (2017), pp. 1011–1028. doi: 10.1007/s11009-016-9510-y
   Web of Science ®Google Scholar
• J. Bulla and I. Bulla, Stylized facts of financial time series and hidden semi-Markov models, Comput. Stat. Data Anal. 51 (2006), pp. 2192–2209. doi: 10.1016/j.csda.2006.07.021
   Web of Science ®Google Scholar
• J. Bulla, I. Bulla, and O. Nenadić, hsmm – an R package for analyzing hidden semi-Markov models, Comput. Stat. Data Anal. 54 (2010), pp. 611–619. doi: 10.1016/j.csda.2008.08.025
   Web of Science ®Google Scholar
• T. Bengtsson and J.E. Cavanaugh, An improved Akaike information criterion for state-space model selection, Comput. Stat. Data Anal. 50 (2006), pp. 2635–2654. doi: 10.1016/j.csda.2005.05.003
   Web of Science ®Google Scholar
• R.A. Bradley and J.J. Gart, The asymptotic properties of ML estimators when sampling from associated populations, Biometrika 49 (1962), pp. 205–214. doi: 10.1093/biomet/49.1-2.205
   Web of Science ®Google Scholar
• R. Calabria and G. Pulcini, Inference and test in modeling the failure/repair process of repairable mechanical equipments, Reliab. Eng. Sys. Safety 67 (2000), pp. 41–53. doi: 10.1016/S0951-8320(99)00045-9
   Web of Science ®Google Scholar
• E. Cepeda-Cuervo and V. Núñez-Antón, Bayesian modelling of the mean and covariance matrix in normal nonlinear models, J. Stat. Comput. Simul. 79 (2000), pp. 837–853. doi: 10.1080/00949650801967403
   Google Scholar
• P. Economou and M. Stehlík, On small samples testing for frailty through homogeneity test, Commun. Stat. Simul. Comput. 44 (2015), pp. 40–65. doi: 10.1080/03610918.2013.763982
   Web of Science ®Google Scholar
• J.K. Filus, On a type of dependencies between Weibull life times of system components, Reliab. Eng. Sys. Safety 31 (1991), pp. 267–280. doi: 10.1016/0951-8320(91)90071-E
   Web of Science ®Google Scholar
• J.K. Filus and L.Z. Filus, On some new classes of multivariate probability distributions, Pak. J. Stat. 1 (2006), pp. 21–42.
   Google Scholar
• J.K. Filus and L.Z. Filus, A method for multivariate probability distributions construction via parameter dependence, Commun. Stat. Theory Methods 42 (2013), pp. 716–721. doi: 10.1080/03610926.2012.731549
   Web of Science ®Google Scholar
• A. Ghosh and A. Basu, Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: The density power divergence approach, J. Appl. Stat. 42 (2015), pp. 2056–2072. doi: 10.1080/02664763.2015.1016901
   Web of Science ®Google Scholar
• C.M. Hurvich and C.L. Tsai, Regression and time series model selection in small samples, Biometrika 76 (1989), pp. 297–307. doi: 10.1093/biomet/76.2.297
   Web of Science ®Google Scholar
• R. Jiang, Introduction to Quality and Reliability Engineering, Springer, Berlin, 2015.
   Google Scholar
• R. Jiang, A Weibull model with time-varying scale parameter for modeling failure processes of repairable systems. In Proc. of the Second International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations Management (SMRLO'16), I. Frenkel, A. Lisnianski, eds., Beer Sheva, Israel, February 15–18, 2016, pp. 292–295, IEEE CPS, 978-1-4673-9941-8/16, doi:10.1109/SMRLO.2016.54.
   Google Scholar
• H. Kim and S. Lee, On first-order integer-valued autoregressive process with Katz family innovations, J. Stat. Comput. Simul. 87 (2017), pp. 546–562. doi: 10.1080/00949655.2016.1219356
   Web of Science ®Google Scholar
• S. Lee and M. Kim, On entropy-based goodness-of-fit test for asymmetric Student-t and exponential power distributions, J. Stat. Comput. Simul. 87 (2017), pp. 187–197. doi: 10.1080/00949655.2016.1196690
   Web of Science ®Google Scholar
• A.A. Neath and J.E. Cavanaugh, A regression model selection criterion based on bootstrap bumping for use with resistant fitting, Comput. Stati. Data Anal. 35 (2000), pp. 155–169. doi: 10.1016/S0167-9473(00)00010-4
   Web of Science ®Google Scholar
• A. Oliveira, T. Oliveira, and A. Seijas-Macías, The uniform distribution product: An approach to the (Q,r) inventory model using R, J. Appl. Stat. 45 (2018), pp. 284–297. doi: 10.1080/02664763.2016.1275531
   Web of Science ®Google Scholar
• J. Orbe and V. Núñez-Antón, Alternative approaches to study lifetime data under different scenarios: From the PH to the modified semiparametric AFT model, Comput. Stat. Data Anal. 50 (2006), pp. 1565–1582. doi: 10.1016/j.csda.2005.01.010
   Web of Science ®Google Scholar
• A Regattieri, Reliability evaluation of manufacturing systems: Methods and applications. In Manufacturing System, F.A. Aziz, ed., InTech, 2012. DOI:10.5772/35653. Available at http://www.intechopen.com/books/manufacturing-system/reliability-evaluation-of-manufacturing-systems-methods-and-applications,
   Google Scholar
• M.J. Schervish, Theory of Statistics, Springer, New York, 1995.
   Google Scholar
• G. Schwarz, Estimating the dimension of a model, Ann. Stat. 6 (1978), pp. 461–464. doi: 10.1214/aos/1176344136
   Web of Science ®Google Scholar
• J. Shang, A multiple comparison procedure based on a variant of the schwarz information criterion in a mixed model, Commun. Stat. Theory Methods 39 (2010), pp. 1095–1109. doi: 10.1080/03610920902846562
   Web of Science ®Google Scholar
• M. Stehlík, Z. Fabián, and L. Stŕelec, Small sample robust testing for normality against Pareto tails, Commun. Stat. Simul. Comput. 41 (2012), pp. 1167–1194. doi: 10.1080/03610918.2012.625849
   Web of Science ®Google Scholar
• T.Y Yang, Measurement of yield distribution: A time-varying distribution model, In Agricultural and Applied Economics Association 2011 Annual Meeting, Pittsburgh, Pennsylvania, July 2011, pp. 24–26,
   Google Scholar
• Y. Zhu, B.K. Goodwin, and S.K. Ghosh, Modeling yield risk under technological change: Dynamic yield distributions and the U.S. crop insurance program, J. Agric. Resour. Econ. 36 (2011), pp. 192–210.
   Web of Science ®Google Scholar