| dBicauchyPR {PosRatioDist} | R Documentation |
BicauchyPR
Description
probability density function of quotient of Bivariate cauchy random variables conditioned to the positive quadrant.For more detailed information please read the first reference paper.
Usage
dBicauchyPR(x, a, b)
Arguments
x |
single real positive scalar |
a |
parameter for bivaraite cauchy distribution |
b |
parameter for bivaraite cauchy distribution |
Details
Probability density function
f_R (r \mid X > 0, Y > 0) =\frac {1}{2 \pi \Pr (X > 0, Y > 0)}J_1 \left( r^2 + 1, A r + B, C, \frac {3}{2} \right)
For -\infty < x < \infty,-\infty < y < \infty,r > 0,-\infty < a < \infty,-\infty < b < \infty,where A = -2 a, B = -2 b,C = 1 + a^2 + b^2 and J_1 is given by first reference paper section (2.5).
Value
dBicauchyPR gives the probability density function for quotient of Bivariate cauchy random variables conditioned to the positive quadrant.
Invalid arguments will return an error message.
Author(s)
Saralees Nadarajah & Yuancheng Si siyuanchengman@gmail.com
References
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.
Balakrishnan, N. and Lai, C. -D. (2009).Continuous Bivariate Distributions.Springer Verlag, New York.
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.
Examples
x <- seq(0.1,5,0.1)
y <- c()
for (i in x){y=c(y,dBicauchyPR(i,1,2))}
plot(x,y,type = 'l')