dBinormalPR {PosRatioDist} | R Documentation |
probability density function of quotient of Bivariate normal random variables conditioned to the positive quadrant.For more detailed information please read the first reference paper.
dBinormalPR(x, a, b, rho)
x |
vector of positive quantiles. |
a |
parameter |
b |
parameter |
rho |
correlation coefficient, |
Probability density function
f_R (r \mid X > 0, Y > 0) =\frac {1}{2 \pi \sqrt{1 - \rho^2} \Pr (X > 0, Y > 0)}\exp \left[ -\frac {a^2 + b^2 - 2 \rho a b}{2 \left( 1 - \rho^2 \right)} \right]I_1 \left( \frac {1 + C r + r^2}{2 \left( 1 - \rho^2 \right)},\frac {A r + B}{2 \left( 1 - \rho^2 \right)} \right)
For -\infty < x < \infty
,-\infty < y < \infty,r > 0,-\infty < a < \infty,-\infty < b < \infty,-1 < \rho < 1
,where A = -2 a + 2 \rho b,B = -2 b + 2 \rho a,C = -2 \rho
dBinormalPR
gives the probability density function for quotient of Bivariate normal random variables conditioned to the positive quadrant.
Invalid arguments will return an error message.
Saralees Nadarajah & Yuancheng Si siyuanchengman@gmail.com
Yuancheng Si and Saralees Nadarajah and Xiaodong Song, (2020). On the distribution of quotient of random variables conditioned to the positive quadrant. Communications in Statistics - Theory and Methods, 49, pp2514-2528.
Balakrishna, N. and Shiji, K. (2014). On a class of bivariate exponential distributions.Statistics and Probability Letters, 85, pp153-160.
Arnold, B. C. and Strauss, D. (1988).Pseudolikelihood estimation.Sankhya B , 53, pp233-243.
Caginalp, C. and Caginalp, G. (2018).The quotient of normal random variables and application to asset price fat tails.Physica A—Statistical Mechanics and Its Applications, 499, pp457-471.
Louzada, F., Ara, A. and Fernandes, G. (2017).The bivariate alpha-skew-normal distribution.Communications in Statistics - Theory and Methods, 46, pp7147-7156.
Nadarajah, S. (2009).A bivariate Pareto model for drought.Stochastic Environmental Research and Risk Assessment, 23, pp811-822.
Nadarajah, S. and Kotz, S. (2006).Reliability models based on bivariate exponential distributions.Probabilistic Engineering Mechanics, 21, pp338-351.
Nadarajah, S. and Kotz, S. (2007).Financial Pareto ratios.Quantitative Finance, 7, pp257-260.
x <- seq(0.1,5,0.1)
y <- dBinormalPR(x, 2, 1, 0.5)
plot(x,y,type = 'l')