Random variable functions used in hydrology

• G. Otiniano, Cira E. ^[1] ; Maluf, Yuri S. ^[1]
  1. [1] Departamento de Estatística, UnB, 70910-900 Brasília, DF, Brazil
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 6, Nº. 2, 2019 (Ejemplar dedicado a: Agosto-Diciembre), págs. 178-188
• Idioma: inglés
• DOI: 10.17268/sel.mat.2019.02.04
• Enlaces
  • Texto completo (pdf)
• Resumen

  • In this work, expressions of the cumulative distribution function of Y X, Y/X and X/(X + Y ) for continuous dependent random variables with supported on a unbounded and bounded interval are derived. The dependence approach is based on copula functions. Additionally, the methodology is applied to real data on hydrology.

• Referencias bibliográficas
  • Ali, M. M., Pal, M., Woo,J. On the ratio of inverted gamma variates, Austrian Journal of Statistics. 2007; 36(2):153-159.
  • Brechmann, E. C., Schepsmeier, U. Modeling dependence with c- and d-vine copulas: The R package CDVine, Journal of Statistical Software. 2013:...
  • U. Cherubini, S. Mulinacci and S. Romagnoli. On the distribution of the (un)bounded sum of random variables, Insurance: Mathematics and Economics,...
  • Clarke, K. A., A simple distribution-free test for nonnested model selection, Political Analysis, 2007; 15:347-363.
  • Dolati,V., Roozegar,R., Ahmadi, N., Shishebor, Z., The effect of dependence on distribution of the functions of random variables, Communications...
  • Domma, F., Giordano, S., A stress-strength model with dependent variables to measure household financial fragility, Statistical Methods &...
  • Domma, F., Giordano, S., A copula-based approach to account for dependence in stress-strength models, Statistical Papers, 2013; 54:807-826.
  • Gupta, A. K., Nadarajah, S., Sums, products and ratios for McKay’s bivariate gamma distributions, Mathematical and Computer Modelling, 2006;...
  • Harry, J., Multivariate Models and Multivariate Dependence Concepts. Chapman and Hall/CRC, 1997.
  • Idrizi, L., On the product and ratio of Pareto and Kumaraswamy random variable, Mathematical Theory and Modeling, 2014; 4(3):136-146.
  • Ljung, G. M., Box, G. E. P., On a measure of lack of fit in time series models, Biometrika, 1978; 65:297-303.
  • Mood, V., Graybill,F., Boes, D., Introduction to the Theory of Statistics. McGraw Hill Inc, 1974.
  • Nadarajah, S., Ali, M. M., Pareto random variables for hydrological modeling, Water Resources Management, 2008; 22:1381-1393.
  • Nadarajah, S., Sums, products and ratios for the bivariate Gumbel distribution, Mathematical and Computer Modelling, 2005; 42:499-518.
  • Nadarajah, S., Sums, products and ratios for the bivariate Lomax distribution, Computational Statistics & Data Analysis, 2005; 49:109-129.
  • Nadarajah, S., Products and ratios for a bivariate gamma distribution, Applied Math ematics and Computation, 2005; 171:581-595.
  • Nadarajah, S., Ali, M. M., The distribution of sums, products and ratios for Lawrance and Lewis’s bivariate exponential random variables,...
  • Nadarajah, S., Dey, D. K., On the product and ratio of t random variables, Applied Mathematics Letters, 2006; 19:45-55.
  • Nadarajah, S., Gupta, A. K., Cherian’s bivariate gamma distribution as a model for drought data, Agrociencia, 2006; 40:483-490.
  • Nadarajah, S., Kotz, S. , Sums, products, and ratios for downton’s bivariate exponential distribution, Stochastic Environmental Research &...
  • Nadarajah, S., The bivariate gamma exponential distribution with application to drought data, Journal of Applied Mathematics and Computing,...
  • Nagar,D. A., Orozco-Castaneda, J. M., Gupta, A. K., Product and quotient of correlated beta variables, Applied Mathematics Letters, 2009;...
  • Nelsen, R. B., An Introduction to Copulas. Springer, 2006.
  • Pham-Gia, T., Distributions of the ratios of independent beta variables and applications, Communications in Statistics - Theory and Methods,...
  • Shakil, M., Golam Kibria, B. M., Exact distribution of the ratio of gamma and Rayleigh random variables, Pakistan Journal of Statistics and...
  • Smith,R. L. , Maximum likelihood estimation in a class of non-regular cases, Biometrika, 1985; 72:67-90.
  • Stuart, C., An Introduction to Statistical Modeling of Extreme Values. Springer, 2001.
  • Trivedi,P. K., Zimmer, D. M., Copulas Modeling: An Introduction for Practitioners. Foundations and Trends in Econometrics, 2005.