PosRatioDist (version 1.2.1)

dBiparetoPR: BiparetoPR

Description

probability density function of quotient of Bivariate Pareto random variables conditioned to the positive quadrant.For more detailed information please read the first reference paper.

Usage

dBiparetoPR(x)

Arguments

x

vector of positive quantiles.

Value

dBiparetoPR gives the probability density function for quotient of Bivariate Pareto random variables conditioned to the positive quadrant.

Invalid arguments will return an error message.

Details

Probability density function $$f_R (r \mid X > 0, Y > 0) = (r + 1)^{-2}$$

For \(r > 0\),Nadarajah (2009) used this distribution to model the proportion of droughts defined as a quotient of drought durations and non-drought durations.

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.

Mardia, K. V. (1962).Multivariate Pareto distributions.Annals of Mathematical Statistics, 33, 1008-1015.

Nadarajah, S. (2009) A bivariate Pareto model for drought.Stochastic Environmental Research and Risk Assessment, 23, pp811-822.

Examples

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

# }