Discrete generalized half-normal distribution and its applications in quantile regression

• Autores: Diego I. Gallardo, Emilio Gómez Déniz , Hector W. Gómez
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 44, Nº. 2, 2020, págs. 265-284
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • A new discrete two-parameter distribution is introduced by discretizing a generalized half-normal distribution. The model is useful for fitting overdispersed as well as underdispersed data. The failure function can be decreasing, bathtub shaped or increasing. A reparameterization of the distribution is introduced for use in a regression model based on the median. The behaviour of the maximum likelihood estimates is studied numerically, showing good performance in finite samples.

    Three real data set applications reveal that the new model can provide a better explanation than some other competitors.

• Referencias bibliográficas
  • Akaike, H. (1974). A new look at statistical model identification, IEEE Transactions on Automatic Control, 19, 716-723.
  • Cameron, A.C. and Trivedi, P.K. (1986). Econometric Models Based on Count Data: Comparisons and Applications of Some Estimators and Tests....
  • Cameron, C. and Trivedi, P.K. (1998). Regression Analysis of Count Data. Cambridge University Press.
  • Chakraborty, S. (2015). Generating discrete analogues of continuous probability distributions-A survey of methods and constructions. Journal...
  • Consul, P.C. and Famoye, F. (1992). Generalized Poisson regression model. Communications in StatisticsTheory and Methods, 21, 89-109.
  • Cooray, K. and Ananda, M. (2008). A Generalization of the Half-Normal Distribution with Applications to Lifetime Data. Communications in Statistics...
  • Dharmadhikari, S. and Joag-Dev, K. (1988).Unimodality, convexity and applications. Probability and mathematical statistics. Academic Press...
  • Frees, E.W. (2010). Regression Models with Actuarial and Financial Applications. Cambridge University Press
  • Gómez-Déniz, E. and Calderı́n, E. (2011). The discrete Lindley distribution: properties and applications. Journal of Statistical Computation...
  • Gómez-Déniz, E., Vázquez-Polo, F.J. and Garcı́a-Garcı́a, V. (2014). A discrete version of the half-normal distribution and its generalization...
  • Heras, A., Moreno, I. and Vilar-Zanón, J.L. (2018). An application of two-stage quantile regression to insurance ratemaking. Scandinavian...
  • Keilson, J. and Gerber, H. (1971). Some results for discrete unimodality. Journal of the American Statistical Association, 66, 386-389.
  • Kemp, A.W. (2008). The discrete half-normal distribution. In: Birkhä (Ed) Advances in mathematical and statistical modeling, pp. 353-365.
  • Koender, R. and Bassett, G. (1978). Regression quantiles. Econometrica, 46, 33-50.
  • Krishna, H. and Singh, P. (2009). Discrete Burr and discrete Pareto distributions. Statistical Methodology, 6, 177-188.
  • Kulasekera, K.B. and Tonkyn, D.W. (1992). A new discrete distribution with applications to survival, dispersal and dispersion. Communications...
  • Lariviere, M.A. and Porteus, E.L. (2001). Selling to the newsvendor: An analysis of price-only contracts. M&SOM, 3, 293-305.
  • Lariviere, M.A. (2006). A note on probability distributions with increasing generalized failure rates. Operations Research, 54 602-604.
  • Marshall, A.W. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential...
  • Nakagawa, T. and Osaki, S. (1975). The discrete Weibull distribution. IEEE Transactions on Reliability, 24, 300-301.
  • R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL...