The Inverse Lomax Distribution

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Description

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

Usage

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dinv.lomax(x, scale = 1, shape2.p, log = FALSE)
pinv.lomax(q, scale = 1, shape2.p, lower.tail = TRUE, log.p = FALSE)
qinv.lomax(p, scale = 1, shape2.p, lower.tail = TRUE, log.p = FALSE)
rinv.lomax(n, scale = 1, shape2.p)

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.

shape2.p

shape parameter.

scale

scale parameter.

log

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

lower.tail, log.p

Same meaning as in pnorm or qnorm.

Details

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

Value

dinv.lomax gives the density, pinv.lomax gives the distribution function, qinv.lomax gives the quantile function, and rinv.lomax generates random deviates.

Note

The inverse Lomax distribution is a special case of the 4-parameter generalized beta II distribution.

Author(s)

T. W. Yee

References

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

See Also

inv.lomax, genbetaII.

Examples

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idata <- data.frame(y = rinv.lomax(n = 1000, exp(2), exp(1)))
fit <- vglm(y ~ 1, inv.lomax, data = idata, trace = TRUE, crit = "coef")
coef(fit, matrix = TRUE)
Coef(fit)

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