Asymptotic behavior of the ratio of weak kth records

References

• Ahsanullah, M., and F. Aliev. 2011. A characterization of geometric distribution based on weak records. Statistical Papers 52 (3):651–5.
   Web of Science ®Google Scholar
• Bairamov, I., and A. Stepanov. 2006. A note on large deviations for weak records. Statistics & Probability Letters 76 (14):1449–53.
   Web of Science ®Google Scholar
• Balakrishnan, N., A. Pakes, and A. Stepanov. 2005. On the number and sum of near record value observations. Advances in Applied Probability 37:1–16.
   Web of Science ®Google Scholar
• Balakrishnan, N., and A. Stepanov. 2008. Asymptotic properties of the ratio of order statistics. Statistics & Probability Letters 78 (3):301–10.
   Web of Science ®Google Scholar
• Bingham, N. H., C. Goldie, and J. F. Teugels. 1987. Regular variation. Cambridge: Cambridge University Press.
   Google Scholar
• Bojanic, R., and E. Seneta. 1973. A unified theory of regularly varying sequences. Mathematische Zeitschrift 134 (2):91–106.
   Web of Science ®Google Scholar
• Castãno-Martinez, A., F. López-Blázquez, and B. Salamanca Miño. 2013. An additive property of weak records from geometric distributions. Metrika 76 (4):449–58.
   Web of Science ®Google Scholar
• Danielak, K., and A. Dembińska. 2007a. Some characterizations of discrete distributions based on weak records. Statistical Papers 48 (3):479–89.
   Web of Science ®Google Scholar
• Danielak, K., and A. Dembińska. 2007b. On characterizing discrete distributions via conditional expectations of weak record values. Metrika 66 (2):129–38.
   Web of Science ®Google Scholar
• Dembińska, A. 2007a. A review on characterizations of discrete distributions based on records and kth records. Communication in Statistics- Theory and Methods 36 (7):1381–7.
   Web of Science ®Google Scholar
• Dembińska, A. 2007b. Characterizations of discrete distributions based on record values. In Extreme value distributions. ed. M. Ahsanullah and S. Kirmani, 63–75. New York: Nova Science Publishers.
   Google Scholar
• Dembińska, A. 2008. Kth records from geometric distribution. Statistics & Probability Letters 78 (12):1662–70.
   Web of Science ®Google Scholar
• Dembińska, A., and K. Danielak. 2008. On moments of k-Records From discrete distributions. Communication in Statistics- Theory and Methods 37 (16):2516–31.
   Web of Science ®Google Scholar
• Dembińska, A., and F. López-Blázquez. 2005a. Kth records from discrete distributions. Statistics & Probability Letters 71 (3):203–14.
   Web of Science ®Google Scholar
• Dembińska, A., and F. López-Blázquez. 2005b. A characterization of geometric distribution through kth weak records. Communication in Statistics- Theory and Methods 34 (12):2345–51.
   Web of Science ®Google Scholar
• Dembińska, A., and A. Stepanov. 2006. Limit theorems for the ratio of weak records. Statistics & Probability Letters 76 (14):1454–64.
   Web of Science ®Google Scholar
• Gouet, R., F. J. López, and G. Sanz. 2007. Asymptotic normality for the counting process of weak records and δ-records in discrete models. Bernoulli 13 (3):754–81.
   Web of Science ®Google Scholar
• Gouet, R., F. J. López, and G. Sanz. 2008. Laws of large numbers for the number of weak records. Statistics & Probability Letters 78 (14):2010–7.
   Web of Science ®Google Scholar
• de Haan, L. 1970. On regular variation and its Applications to the Weak Convergence of Sample Extremes. No. 3 of Mathematicae Centre Tract. Amsterdam.
   Google Scholar
• Hijab, O., and M. Ahsanullah. 2006. Weak records of geometric distributions and some characterizations. Pakistan Journal of Statistics 22 (2):139–46.
   Google Scholar
• Hashorva, E., and A. Stepanov. 2012. Limit theorems for the spacings of weak records. Metrika 75 (2):163–80.
   Web of Science ®Google Scholar
• Jasiński, K. 2018. Relations for product moments and covariances of kth records from discrete distributions. Metrika 81 (2):125–41.
   Web of Science ®Google Scholar
• Karczewski, R., and J. Wesołowski. 2017. Linearity of regression for weak records, revisited. Statistics 51 (4):878–87.
   Web of Science ®Google Scholar
• Key, E. S. 2005. On the number of records in an iid discrete sequence. Journal of Theoretical Probability 18 (1):99–107.
   Web of Science ®Google Scholar
• López-Blázquez, F., and J. Wesołowski. 2001. Discrete distributions for which the regression of the first record on the second is linear. Test 10 (1):121–31.
   Web of Science ®Google Scholar
• López-Blázquez, F., B. Salamanca Miño, and A. Dembińska. 2005. A note on the distribution of kth records from discrete distributions. Statistics & Probability Letters 75 (4):325–30.
   Web of Science ®Google Scholar
• Resnick, S. I. 1987. Extreme values, regular variation, and point processes. New York: Springer.
   Google Scholar
• Seneta, E. 1976. Regularly varying functions. Vol. 3 of lectures notes in mathematics. Berlin: Springer.
   Google Scholar
• Shorrock, R. W. 1972. On record values and record times. Journal of Applied Probability 9 (2):316–26.
   Web of Science ®Google Scholar
• Stepanov, A. V. 1993. Limit theorems for weak records. Theory of Probability & Its Applications 37 (3):570–4.
   Web of Science ®Google Scholar
• Vervaat, W. 1973. Limit theorems for records from discrete distributions. Stochastic Processes and Their Applications 1 (4):317–34.
   Google Scholar
• Wesołowski, J., and M. Ahsanullah. 2001. Linearity of regression for non-adjacent weak records. Statistica Sinica 11 (1):39–52.
   Web of Science ®Google Scholar
• Wesołowski, J., and F. López-Blázquez. 2004. Linearity of regression for the past weak and ordinary records. Statistics 38 (6):457–64.
   Web of Science ®Google Scholar