VGAM (version 0.9-1)

Invparalogistic: The Inverse Paralogistic Distribution

Description

Density, distribution function, quantile function and random generation for the inverse paralogistic distribution with shape parameters a and p, and scale parameter scale.

Usage

dinvparalogistic(x, shape1.a, scale = 1, log = FALSE)
pinvparalogistic(q, shape1.a, scale = 1)
qinvparalogistic(p, shape1.a, scale = 1)
rinvparalogistic(n, shape1.a, scale = 1)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

shape1.a

shape parameter.

scale

scale parameter.

log

Logical. If log = TRUE then the logarithm of the density is returned.

Value

• dinvparalogistic gives the density, pinvparalogistic gives the distribution function, qinvparalogistic gives the quantile function, and rinvparalogistic generates random deviates.

Details

See invparalogistic, which is the VGAM family function for estimating the parameters by maximum likelihood estimation.

References

Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ, USA: Wiley-Interscience.

See Also

invparalogistic, genbetaII.

Examples

idata <- data.frame(y = rinvparalogistic(n = 3000, exp(1), exp(2)))
fit <- vglm(y ~ 1, invparalogistic(ishape1.a = 2.1),
            idata, trace = TRUE, crit = "coef")
coef(fit, matrix = TRUE)
Coef(fit)