The Inverse Lomax Distribution

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

Usage

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.

Value

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

References

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

Author

T. W. Yee

Details

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

Note

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

Examples

idata <- data.frame(y = rinv.lomax(n = 1000, exp(2), exp(1)))
fit <- vglm(y ~ 1, inv.lomax, idata, trace = TRUE, crit = "coef")
#> Iteration 1: coefficients = 2.06389546, 0.96741576
#> Iteration 2: coefficients = 2.06457284, 0.96720349
#> Iteration 3: coefficients = 2.06458900, 0.96719182
#> Iteration 4: coefficients = 2.06458939, 0.96719154
#> Iteration 5: coefficients = 2.06458940, 0.96719154
coef(fit, matrix = TRUE)
#>             loglink(scale) loglink(shape2.p)
#> (Intercept)       2.064589         0.9671915
Coef(fit)
#>    scale shape2.p 
#> 7.882061 2.630546