| dBiMG_expPR {PosRatioDist} | R Documentation |
BiMG_expPR
Description
probability density function of quotient of Morgenstern type bivariate exponential random variables conditioned to the positive quadrant.For more detailed information please read the first reference paper.
Usage
dBiMG_expPR(x, a, b, alpha)
Arguments
x |
vector of positive quantiles. |
a |
parameter for Morgenstern type bivariate exponential distribution |
b |
parameter for Morgenstern type bivariate exponential distribution |
alpha |
parameter for Morgenstern type bivariate exponential distribution |
Details
Probability density function
f_R (r \mid X > 0, Y > 0) = \frac {(1 + \alpha) \exp (a + b)}{\Pr (X > 0, Y > 0) (1 + r)^2} - \frac {2 \alpha \exp (a + 2 b)}{\Pr (X > 0, Y > 0) (2 + r)^2} - \frac {2 \alpha \exp (2 a + b)}{\Pr (X > 0, Y > 0) (1 + 2 r)^2} + \frac {\alpha \exp (2 a + 2 b)}{\Pr (X > 0, Y > 0) (1 + r)^2}
For r > 0,-1 \leq \alpha \leq 1, a > -\infty, b > -\infty These correlated exponential random variables can also be used to model the stress and strength components of a system, hence the quotient distribution can be used to estimate the probability of failure of the system
Value
dBiMG_expPR gives the probability density function for quotient of Morgenstern type bivariate exponential 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.
Balakrishna, N. and Shiji, K. (2014).On a class of bivariate exponential distributions.Statistics and Probability Letters, 85, pp153-160.
Examples
x <- seq(0.1,5,0.1)
y <- dBiMG_expPR(x, 3, 2, 0.5)
plot(x,y,type = 'l')