PosRatioDist (version 1.2.1)

dBibs_expPR: Bibs_expPR

Description

probability density function of quotient of Balakrishna and Shiji's bivariate exponential random variables conditioned to the positive quadrant.For more detailed information please read the first reference paper.

Usage

dBibs_expPR(x, a, r)

Arguments

x

vector of positive quantiles.

a

parameter for Balakrishna and Shiji's bivariate exponential distribution

r

parameter for Balakrishna and Shiji's bivariate exponential distribution

Value

dBibs_expPR gives the probability density function for quotient of Balakrishna and Shiji's bivariate exponential random variables conditioned to the positive quadrant.

Invalid arguments will return an error message.

Details

Probability density function $$f_R (r \mid X > 0, Y > 0) = \frac {a}{2 \sqrt{r}} \left( r + \frac {a^2}{4 r} \right)^{-3 / 2}$$

For \(r > 0\),\(a > 0\)

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

# NOT RUN {
x <- seq(0.1,5,0.1)
y <- dBibs_expPR(x, 2, 2)
plot(x,y,type = 'l')
# }