dBiexpweightedPR {PosRatioDist}

BiexpweightedPR

Description

probability density function of quotient of Bivariate exponential random variables resulting from weighted linear combinations conditioned to the positive quadrant.For more detailed information please read the first reference paper.

Usage

dBiexpweightedPR(x, a, b, c)

Arguments

x

vector of positive quantiles.

a

parameter for Bivariate exponential random variables resulting from weighted linear combinations

b

parameter for Bivariate exponential random variables resulting from weighted linear combinations

c

parameter for Bivariate exponential random variables resulting from weighted linear combinations

Details

Probability density function

f_R (r \mid X > 0, Y > 0) = \frac {(1 - 2 c) \exp \left[ (1 - 2 c) a + b \right]} {\Pr (X > 0, Y > 0) \left[ 1 + (1 - 2 c) r \right]^2}

For x > a > -\infty,y > b > -\infty,r > 0,0 < c < 1,These correlated exponential random variables can 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

dBiexpweightedPR gives the probability density function for quotient of Bivariate exponential random variables resulting from weighted linear combinations conditioned to the positive quadrant.

Invalid arguments will return an error message.

Author(s)

Saralees Nadarajah & Yuancheng Si [e-mail]

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 <- dBiexpweightedPR(x, 4, 2, 0.2)
plot(x,y,type = 'l')