On the modes of the negative binomial distribution of order k, type I

References

• Arapis, A. N., F. S. Makri, and Z. M. Psillakis. 2018. Distributions of statistics describing concentration of runs in non homogeneous Markov-dependent trials. Communications in Statistics – Theory and Methods 47 (9):2238–50. doi:10.1080/03610926.2017.1337144.
   Web of Science ®Google Scholar
• Balakrishnan, N., and M. V. Koutras. 2002. Runs and scans with applications. New York: Wiley.
   Google Scholar
• Dodge, H. F. 1943. A sampling inspection plan for continuous production. The Annals of Mathematical Statistics 14 (3):264–79. doi:10.1214/aoms/1177731420.
   Google Scholar
• Eryilmaz, S. 2016. Generalized waiting time distributions associated with runs. Metrika 79 (3):357–68. doi:10.1007/s00184-015-0558-4.
   Web of Science ®Google Scholar
• Eryilmaz, S. 2017. A new class of bivariate lifetime distributions. Communications in Statistics – Theory and Methods 46 (24):12324–35. doi:10.1080/03610926.2017.1295078.
   Web of Science ®Google Scholar
• Eryilmaz, S. 2018. On success runs in a sequence of dependent trials with a change point. Statistics and Probability Letters 132 :91–8. doi:10.1016/j.spl.2017.09.007.
   Web of Science ®Google Scholar
• Feller, W. 1968. An introduction to probability theory and its applications. New York: Wiley.
   Google Scholar
• Georghiou, C., A. N. Philippou, and A. Saghafi. 2013. On the modes of the Poisson distribution of order k. The Fibonacci Quarterly 51 :44–8.
   Google Scholar
• Ghahramani, S. 2016. Fundamentals of probability with stochastic processes. 3rd ed. Boca Raton:Taylor and Francis.
   Google Scholar
• Godbole, A. P. 1990. Specific formulae for some success run distributions. Statistics and Probability Letters 10 (2):119–24. doi:10.1016/0167-7152(90)90006-S.
   Web of Science ®Google Scholar
• Govindaraju, K., and S. Balamurali. 1998. Tightened single-level continuous sampling plan. Journal of Applied Statistics 25 (4):451–61. doi:10.1080/02664769822945.
   Web of Science ®Google Scholar
• Inoue, K., and S. Aki. 2003. Generalized binomial and negative binomial distributions of order k by the ℓ-overlapping enumeration scheme. Annals of the Institute of Statistical Mathematics 55: 153–67. doi:10.1007/BF02530491.
   Web of Science ®Google Scholar
• Koutras, M. V., and S. Eryilmaz. 2017. Compound geometric distribution of order k. Methodology and Computing in Applied Probability 19 (2):377–93. doi:10.1007/s11009-016-9482-y.
   Web of Science ®Google Scholar
• Makri, F. S., A. N. Philippou, and Z. M. Psillakis. 2007. Polya, inverse polya, and circular polya distributions of order k for ℓ-overlapping success runs. Communications in Statistics – Theory and Methods 36 :657–68. doi:10.1080/03610920601033942.
   Web of Science ®Google Scholar
• Mytalas, G. C., and M. A. Zazanis. 2013. Central limit theorem approximations for the number of runs in Markov-dependent binary sequences. Journal of Statistical Planning and Inference 143(2):321–33. doi:10.1016/j.jspi.2012.07.014.
   Web of Science ®Google Scholar
• Pervez, Z., F. S. Shah, Z. Hussain, and A. N. Philippou. 2017. An application of negative binomial distribution of orger k in sensitive surveys. Communications in Statistics – Simulation and Computation 46 (8):6654–60. doi:10.1080/03610918.2016.1248570.
   Web of Science ®Google Scholar
• Philippou, A. N. 1984. The negative binomial distribution of order k and some of its properties. Biometrical Journal 26 (7):789–94. doi:10.1002/bimj.4710260719.
   Web of Science ®Google Scholar
• Philippou, A. N. 2014. A note on the modes of the poisson distribution of order k. The Fibonacci Quarterly 52 :203–5.
   Google Scholar
• Philippou, A. N., and D. L. Antzoulakos. 2011. Distributions of order k. In: International encyclopedia of statistical science, ed. M. Lovric, Berlin: Springer-Verlag, 400–2.
   Google Scholar
• Philippou, A. N., and C. Georghiou. 1989. Convolutions of Fibonacci-type polynomials of order k and the negative binomial distributions of the same order. The Fibonacci Quarterly 27: 209–16.
   Web of Science ®Google Scholar
• Philippou, A. N., C. Georghiou, and G. N. Philippou. 1983. A generalized geometric distribution and some of its properties. Statistics and Probability Letters 1(4):171–5. doi:10.1016/0167-7152(83)90025-1.
   Google Scholar
• Shao, J., and S. Fu. 2016. On the modes of the negative binomial distribution of order k. Journal of Applied Statistics 43 (11):2131–49. doi:10.1080/02664763.2015.1130802.
   Web of Science ®Google Scholar
• Suresh, K. K., and V. Nirmala. 2015. Comparison of certain types of continuous sampling plans (CPSs) and its operating procedures - a review. International Journal of Science and Research 4:455–9.
   Google Scholar