pearson7 (version 1.0-3)

ppearson7: Evaluate the distribution function for the Pearson VII distribution with shape parameter 3/2.

Description

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

Usage

ppearson7(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

q

vector of quantiles.

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 probability.

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 cdf $$F(x)=\{1+(x-\mu)/\sqrt{\sigma^2+(x-\mu)^2}\}/2.$$

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, qpearson7, rpearson7

Examples

# NOT RUN {
curve(ppearson7(x), 0, 5, lwd = 2, ylim = c(0.8, 1), ylab = "F(x)")
curve(pnorm(x), lwd = 2, lty = 2, add = TRUE)

# }