dBitPR {PosRatioDist} | R Documentation |
BitPR
Description
probability density function of quotient of Bivariate t random variables conditioned to the positive quadrant.For more detailed information please read the first reference paper.
Usage
dBitPR(x, a, b, rho, v)
Arguments
x |
single positive scalar,for quotient of Bivariate t random variables conditioned to the positive quadrant |
a |
parameter for Bivariate t distribution |
b |
parameter for Bivariate t distribution |
rho |
correlation coefficient, |
v |
parameter, degree of freedom of Bivariate t distribution |
Details
Probability density function
For ,
,where
and
is given by first reference paper section (2.5).
Value
dBitPR
gives the probability density function for quotient of Bivariate t 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.
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.
Examples
x <- seq(0.1,5,0.1)
y <- c()
for (i in x){y=c(y,dBitPR(i,1,2,0.5,2))}
plot(x,y,type = 'l')