The Geometric ArcTan distribution with applications to model demand for health services

References

• Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (6):716–23.
   Google Scholar
• Bozdogan, H. 1987. The general theory and its analytical extension. Psychometrika 52 (3):345–70.
   Google Scholar
• Chakraborty, S., and D. Bhati. 2016. Transmuted geometric distribution with applications in modeling and regression analysis of count data. SORT (Statistics and Operations Research Transactions) 40 (1):153–76.
   Google Scholar
• Chakraborty, S., and R. Gupta. 2012. Exponentiated geometric distribution: Another generalization of geometric distribution. Communications in Statistics-Theory and Methods 44:1143–157.
   Google Scholar
• Deb, P., and P. Trivedi. 1997. Demand for medical care by the elderly: A finite mixture approach. Journal of Applied Econometrics 12 (3):313–36.
   Google Scholar
• Farrington, C., and D. Grant. 1999. The distribution of time to extinction in subcritical branching process: Applications to outbreak of infectious disease. Journal of Applied Probability 36:771–79.
   Google Scholar
• Gómez-Déniz, E. 2010. Another generalization of the geometric distribution. Test 19:399–405.
   Google Scholar
• Gómez-Déniz, E., and E. Calderín. 2015a. Modelling insurance data with the Pareto ArcTan distribution. ASTIN BULLETIN 45 (3):639–60.
   Google Scholar
• Gómez-Déniz, E., and E. Calderín. 2015b. On the use of the Pareto ArcTan distribution for describing city size in australia and new zealand. Physica A 436:821–32.
   Google Scholar
• Gómez-Déniz, E., J. Sarabia, and E. Calderín. 2011. A new discrete distribution with actuarial applications. Insurance: Mathematics and Economics 48:406–12.
   Google Scholar
• Gupta, P., R. Gupta, and R. Tripathi. 1997. On the monotonic properties of discrete failure rates. Journal of Statistical Planning and Inference 65:255–68.
   Google Scholar
• Jacob, E., and Jayakumar, K. 2012. On half-Cauchy distribution and process. Journal of Statistika and Mathematika 3(2):77–81.
   Google Scholar
• Jain, G., and P. Consul. 1971. A generalized negative binomial distribution. Siam Journal of Applied Mathematics 21:501–13.
   Google Scholar
• Johnson, N., A. Kemp, and S. Kotz. 2005. Univariate discrete distributions. New York: John Wiley, INC.
   Google Scholar
• Karlis, D. 2005. EM algorithm for mixed Poisson and other discrete distributions. ASTIN Bulletin 35 (1):3–24.
   Google Scholar
• Keilson, J., and H. Gerber. 1971. Some results for discrete unimodality. Journal of the American Statistical Association 66 (334):386–89.
   Google Scholar
• Komárek, A., E. Lesaffre, T. Harkanen, D. Decklerck, and J. Virtanen. 2005. A bayesian analysis of multivariate doubly-interval-censored dental data. Biostatistics 6:145–55.
   Google Scholar
• Krishna, H., and P. Pundir. 2009. Discrete Burr and discrete Pareto distributions. Statistical Methodology 6:177–88.
   Google Scholar
• Makcutek, J. 2008. A generalization of the geometric distribution and its application in quantitative linguistics. Romanian Reports in Physics 60 (3):501–509.
   Google Scholar
• Marshall, A., and I. Olkin. 1997. A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84 (3):641–52.
   Google Scholar
• Philippou, A., C. Georghiou, and G. Philippou. 1983. A generalized geometric distribution and some of its properties. Statistics & Probability Letters 1:171–75.
   Google Scholar
• Qi, F., S.-Q. Zhang, and B.-N. Guo. 2009. Inequality for the Arc Tangent function. Journal of Inequalities and Applications 1–9.
   Google Scholar
• Rajan, S., S. Wang, R. Inkol, and A. Joyal. 2006. Efficient approximations for the arctangent function. IEEE Signal Processing Magazine 23 (3):108–11.
   Google Scholar
• Sastry, D., D. Bhati, R. Rattihalli, and E. Gómez-Déniz. 2016. On zero distorted generalised geometric distribution. Communications in Statistics-Theory and Methods 45 (18):5427–442.
   Google Scholar
• Tripathi, R., R. Gupta, and T. White. 1987. Some generalizations of the geometric distribution. Sankhy$\bar{\text{a}}$, Series B 49 (3):218–23.
   Google Scholar
• Vanobberger, J., L. Martens, E. Lesaffre, and D. Declerck. 2000. The Signal-Tandmobiel project -a longitudinal intervention health promotion study in Flanders (Belgium): Baseline and first source results. European Journal of Paediatric Dentistry 2:87–96.
   Google Scholar
• Xie, M., O. Gaudoin, and C. Bracquemond. 2002. Redefining failure rate function for discrete distributions. International Journal of Reliability, Quality and Safety Engineering 9:275–85.
   Google Scholar