On the Distribution of the Product of Inverse Pareto and Exponential Random Variables
Keywords:product distribution, inverse Pareto, exponential
This article considers Inverse Pareto and Exponential distributions to create the distribution of the product. The researchers derived its properties, such as; survival functions and hazard functions, and used the model criterion such as Sum Square Error (SSE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) in estimating the parameters for deriving the best joint distribution between monthly precipitation and temperature in the Philippines from 1974 to 2013. The results showed that considering the monthly precipitation and temperature data, the distribution of the product of Inverse Pareto and Exponential outperformed the other existing distribution of the product.
Arcede, J. P., & Macalos, M. O. (2016). On the distribution of the sums, products and quotient of lomax distributed random variables based on FGM copula. Annals of Studies in Science and Humanities, 1(2), 60–74.
Feldstein, M. S. (1971). The error of forecast in econometric models when the forecast-period exogenous variables are stochastic. Econometrica, 39(1), 55. https://doi.org/10.2307/1909139
Gradshteyn, I. S., & Ryzhik, I. M. (2014). Table of integrals, series, and products. Academic Press. https://doi.org/10.1016/c2010-0-64839-5
Grubel, H. G. (1968). Internationally diversified portfolios: Welfare gains and capital flows. The American Economic Review, 58(5), 1299–1314.
Ly, S., Pho, K.-H., Ly, S., & Wong, W.-K. (2019). Determining distribution for the quotients of dependent and independent random variables by using copulas. Journal of Risk and Financial Management, 12(1), 42. https://doi.org/10.3390/jrfm12010042
Malik, H. J., & Trudel, R. (1986). Probability density function of the product and quotient of two correlated exponential random variables. Canadian Mathematical Bulletin, 29(4), 413–418. https://doi.org/10.4153/cmb-1986-065-3
Nadarajah, S., & Espejo, M. R. (2006). Sums, products, and ratios for the generalized bivariate Pareto distribution. Kodai Mathematical Journal, 29(1), 72–83. https://doi.org/10.2996/kmj/1143122388
NASA Langley Research Center. (n.d.). NASA POWER data access viewer. https://power.larc.nasa.gov/data-access-viewer/
Pizon, M. G., & Arcede, J. P. (2018). On the distribution of the products and quotient of inverse Burr distributed random variables based on FGM Copula. Journal of Higher Education Research Disciplines, 3(2). https://www.nmsc.edu.ph/ojs/index.php/jherd/article/view/117
Pizon, M. G., & Paluga, R. N. (2022). A special case of Rodriguez-Lallena and Ubeda-Flores copula based on Ruschendorf method. Applications and Applied Mathematics, 17(1), 18–22. https://digitalcommons.pvamu.edu/aam/vol17/iss1/2/
Sakamoto, H. (1943). On the distributions of the product and the quotient of the independent and uniformly distributed random variables. Tohoku Mathematical Journal, First Series, 49, 243–260.
Stuart, A. (1962). Gamma-distributed products of independent random variables. Biometrika, 49(3-4), 564–565. https://doi.org/10.1093/biomet/49.3-4.564
Tang, J., & Gupta, A. K. (1984). On the distribution of the product of independent beta random variables. Statistics & Probability Letters, 2(3), 165–168. https://doi.org/10.1016/0167-7152(84)90008-7
Thomas, N. M. (2013). Distribution of products of independently distributed pathway random variables. Statistics, 47(4), 861–875. https://doi.org/10.1080/02331888.2011.631707
Tse, D., & Viswanath, P. (2005). Fundamentals of wireless communication. Cambridge University Press.
Wallgren, C. M. (1980). The distribution of the product of two correlated t variates. Journal of the American Statistical Association, 75(372), 996–1000. https://doi.org/10.1080/01621459.1980.10477585
How to Cite
Copyright (c) 2023 University of San Jose-Recoletos
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Copyright of the Journal belongs to the University of San Jose-Recoletos