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Research Article

Time-dependent residual Fisher information and distance for some special continuous distributions

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Received 11 May 2022, Accepted 03 Nov 2022, Published online: 21 Nov 2022

References

  • Aalen, O. O. 1988. Heterogeneity in survival analysis. Statistics in Medicine 7 (11):1121–37. doi:10.1002/sim.4780071105.
  • Arellano-Valle, R. B., J. E. Contreras-Reyes, and M. Stehlík. 2017. Generalized skew-normal negentropy and its application to fish condition factor time series. Entropy 19 (10):528. doi:10.3390/e19100528.
  • Azzalini, A. 2013. The skew-normal and related families, vol. 3. Cambridge, UK: Cambridge University Press.
  • Barlow, R. E, and F. Proschan. 1981. Statistical theory or reliability and life testing: Probability models. New York-Montreal, Que.-London: Holt, Rinehart and Winston, Inc. MR0438625.
  • Bauckhage, C. 2014. Computing the Kullback–Leibler divergence between two generalized gamma distributions. arXiv preprint arXiv:1401.6853.
  • Barndorff-Nielsen, O. E. 1997. Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of Statistics 24:1–13.
  • Bhaumik, D. K., K. Kapur, and R. D. Gibbons. 2009. Testing parameters of a gamma distribution for small samples. Technometrics 51 (3):326–34. doi:10.1198/tech.2009.07038.
  • Caamaño-Carrillo, C, and J. E. Contreras-Reyes. 2022. A generalization of the bivariate gamma distribution based on generalized hypergeometric functions. Mathematics 10 (9):1502. doi:10.3390/math10091502.
  • Contreras-Reyes, J. E. 2015. Rényi entropy and complexity measure for skew-Gaussian distributions and related families. Physica A.433:84–91. doi:10.1016/j.physa.2015.03.083.
  • Contreras-Reyes, J. E. 2021. Fisher information and uncertainty principle for skew-Gaussian random variables. Fluctuation and Noise Letters 20 (5):2150039. doi:10.1142/S0219477521500395.
  • Contreras-Reyes, J. E. 2022. Information-theoretic aspects of location parameter estimation under skew-normal settings. Entropy 24 (3):399. doi:10.3390/e24030399.
  • Contreras-Reyes, J. E., M. Maleki, and D. D. Cortés. 2019. Skew-reflected-Gompertz information quantifiers with application to sea surface temperature records. Mathematics 7 (5):403. doi:10.3390/math7050403.
  • Contreras-Reyes, J. E., F. Kahrari, and D. D. Cortés. 2021. On the modified skew-normal-Cauchy distribution: Properties, inference and applications. Communications in Statistics - Theory and Methods 50 (15):3615–31. doi:10.1080/03610926.2019.1708942.
  • Cover, T. M, and J. A. Thomas. 2006. Elements of information theory. 2nd ed. New York, NY: Wiley & Son, Inc.
  • Dembo, A., T. M. Cover, and J. A. Thomas. 1991. Information theoretic inequalities. IEEE Transactions on Information Theory 37 (6):1501–18. doi:10.1109/18.104312.
  • Dubey, S. D. 1970. Compound gamma, beta and F distributions. Metrika 16 (1):27–31. doi:10.1007/BF02613934.
  • Flecher, C., D. Allard, and P. Naveau. 2010. Truncated skew-normal distributions: Moments, estimation by weighted moments and application to climatic data. METRON 68 (3):331–45. doi:10.1007/BF03263543.
  • Gradshteyn, I. S, and I. M. Ryzhik. 2014. Table of integrals, series, and products. Cambridge, MA, USA: Academic Press.
  • Hürlimann, W. 2013. Tail approximation of the skew-normal by the skew-normal Laplace: Application to Owen’s T function and the bivariate normal distribution. Journal of Statistical and Economic Method 2:1–12.
  • Jamalizadeh, A., R. Pourmousa, and N. Balakrishnan. 2009. Truncated and limited skew-normal and skew-t distributions: Properties and an illustration. Communications in Statistics – Theory and Methods 38 (16-17):2653–68. doi:10.1080/03610910902936109.
  • Johnson, N. L., S. Kotz, and N. Balakrishnan. 1995. Continuous univariate distributions. 2nd ed. New York, NY, USA: John Wiley & Sons, Inc.
  • Jørgensen, B. 2012. Statistical properties of the generalized inverse Gaussian distribution. Lecture notes in statistics. vol. 9. New York-Berlin: Springer-Verlag.
  • Kharazmi, O, and M. Asadi. 2018. On the time-dependent Fisher information of a density function. Brazilian Journal of Probability and Statistics 32:795–814.
  • Kharazmi, O, and N. Balakrishnan. 2021. Cumulative residual and relative cumulative residual Fisher information and their properties. IEEE Transactions on Information Theory 67 (10):6306–12. doi:10.1109/TIT.2021.3073789.
  • Kim, H. J. 2008. Moments of truncated student-t distribution. Journal of the Korean Statistical Society 37 (1):81–7. doi:10.1016/j.jkss.2007.06.001.
  • Mudholkar, G. S., D. K. Srivastava, and G. D. Kollia. 1996. A generalization of the Weibull distribution with application to the analysis of survival data. Journal of the American Statistical Association 91 (436):1575–83. doi:10.1080/01621459.1996.10476725.
  • Nakagami, M. 1960. The m-Distribution, a general formula of intensity of rapid fading. In Statistical methods in radio wave propagation: Proceedings of a Symposium Held at the University of California, Los Angeles, USA, June 18–20, 1958, ed. William C. Hoffman, 3–36. Pergamon Press.
  • Owen, D. B. 1980. A table of normal integrals. Communications in Statistics - Simulation and Computation 9 (4):389–419. doi:10.1080/03610918008812164.
  • Pennini, F., A. Plastino, B. H. Soffer, and C. Vignat. 2009. Physical symmetries and Fisher’s information measure. Physics Letters A 373 (8-9):817–20. doi:10.1016/j.physleta.2009.01.007.
  • R Core Team. 2021. A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. http://www.R-project.org.
  • Small, C. G. 2010. Expansions and asymptotics for statistics. Boca Raton, FL, USA: Chapman and Hall/CRC.
  • Stacy, E. W. 1962. A generalization of the gamma distribution. The Annals of Mathematical Statistics 33 (3):1187–92. doi:10.1214/aoms/1177704481.

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