# beniniUC: The Benini Distribution

### Description

Density, distribution function, quantile function and random generation for the Benini distribution with parameter `shape`.

### Usage

 ```1 2 3 4``` ```dbenini(x, y0, shape, log = FALSE) pbenini(q, y0, shape, lower.tail = TRUE, log.p = FALSE) qbenini(p, y0, shape, lower.tail = TRUE, log.p = FALSE) rbenini(n, y0, shape) ```

### Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of observations. Same as `runif`. `y0` the scale parameter y0. `shape` the shape parameter b. `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 `benini1`, the VGAM family function for estimating the parameter s by maximum likelihood estimation, for the formula of the probability density function and other details.

### Value

`dbenini` gives the density, `pbenini` gives the distribution function, `qbenini` gives the quantile function, and `rbenini` generates random deviates.

### Author(s)

T. W. Yee and Kai Huang

### References

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

`benini1`.

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```## Not run: y0 <- 1; shape <- exp(1) xx <- seq(0.0, 4, len = 101) plot(xx, dbenini(xx, y0 = y0, shape = shape), type = "l", col = "blue", main = "Blue is density, orange is cumulative distribution function", sub = "Purple lines are the 10,20,...,90 percentiles", ylim = 0:1, las = 1, ylab = "", xlab = "x") abline(h = 0, col = "blue", lty = 2) lines(xx, pbenini(xx, y0 = y0, shape = shape), col = "orange") probs <- seq(0.1, 0.9, by = 0.1) Q <- qbenini(probs, y0 = y0, shape = shape) lines(Q, dbenini(Q, y0 = y0, shape = shape), col = "purple", lty = 3, type = "h") pbenini(Q, y0 = y0, shape = shape) - probs # Should be all zero ## End(Not run) ```

Search within the VGAM package
Search all R packages, documentation and source code

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

Please suggest features or report bugs with the GitHub issue tracker.

All documentation is copyright its authors; we didn't write any of that.