Random variable functions used in hydrology
DOI:
https://doi.org/10.17268/sel.mat.2019.02.04Palavras-chave:
Product, Ratio, Copula, HydrologyResumo
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.Referências
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: 52(3):1-27.
U. Cherubini, S. Mulinacci and S. Romagnoli. On the distribution of the (un)bounded sum of random variables, Insurance: Mathematics and Economics, 2011; 48:56-63.
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 in Statistics - Theory and Methods, 2007; 46:10704-10717.
Domma, F., Giordano, S., A stress-strength model with dependent variables to measure household financial fragility, Statistical Methods & Applications, 2012; 21:375-389.
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; 43:185-193.
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, Computational Statistics & Data Analysis, 2006; 50:3449-3463.
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 & Risk Assessment, 2006; 20:164-170.
Nadarajah, S., The bivariate gamma exponential distribution with application to drought data, Journal of Applied Mathematics and Computing, 2007; 24:221-230.
Nagar,D. A., Orozco-Castaneda, J. M., Gupta, A. K., Product and quotient of correlated beta variables, Applied Mathematics Letters, 2009; 22:105-109.
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, 2000; 29(12):2693-2715.
Shakil, M., Golam Kibria, B. M., Exact distribution of the ratio of gamma and Rayleigh random variables, Pakistan Journal of Statistics and Operation Research, 2006; 2(2):87-98.
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.
Downloads
Publicado
Como Citar
Edição
Seção
Licença
Os autores que publicam nesta revista aceitam as seguintes condições:
Os autores mantêm os direitos autorais e atribuem à revista o direito da primeira publicação, com o trabalho registrado com a licença de atribuição Creative Commons Atribución 4.0 Internacional (CC BY 4.0), que permite que terceiros usem o material publicado sempre que mencionarem a autoria do trabalho e os direitos autorais. Primeira publicação nesta revista.
Os autores podem fazer outros acordos contratuais independentes e adicionais para a distribuição não exclusiva da versão do artigo publicada nesta revista (por exemplo, incluí-la em um repositório institucional ou publicá-la em um livro), desde que afirme claramente que o trabalho Foi publicado nesta revista.
É permitido e recomendado aos autores que publiquem seus trabalhos na Internet (por exemplo, em páginas institucionais ou pessoais) antes e durante o processo de revisão e publicação, pois isso pode levar a trocas produtivas e a uma disseminação maior e mais rápida do trabalho. publicado (Consultar: efeito do acesso aberto).