# inv.lomaxUC: The Inverse Lomax Distribution

### Description

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

### Usage

 ```1 2 3 4``` ```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.

T. W. Yee

### References

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

`inv.lomax`, `genbetaII`.

### Examples

 ```1 2 3 4``` ```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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