pearson7 (version 1.0-3)

qpearson7: Evaluate the quantile function for the Pearson VII distribution with shape parameter 3/2.

Description

Evaluate the quantile function for the Pearson VII distribution with shape parameter 3/2.

Usage

qpearson7(p, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

p

vector of probabilities.

mu

vector of means.

sigma

vector of scales.

lower.tail

logical; if TRUE (default), probabilities are \(P(X\le x)\), otherwise \(P(X>x)\).

log.p

logical; if TRUE, probabilities p are given as log(p).

Value

the quantile.

Details

If mu is not specified, it assumes the default value of 0. If sigma is not specified, it assumes the default value of 1.

The Pearson VII distribution with location \(\mu\), scale \(\sigma\), and shape 3/2 has quantile function $$F^{-1}(x)=\mu+(\sigma/2)(2x-1)/\sqrt{x(1-x)}.$$

References

Hughes, J., Shastry, S., Hancock, W. O., and Fricks, J. (2013) Estimating velocity for processive motor proteins with random detachment. Journal of Agricultural, Biological, and Environmental Statistics, in press.

See Also

dpearson7, ppearson7, rpearson7

Examples

# NOT RUN {
curve(qpearson7(x), 0, 1, lwd = 2, ylab = expression(F^{-1}*(x)))
curve(qnorm(x), lwd = 2, lty = 2, n = 500, add = TRUE)

# }