VGAM: beniniUC – R documentation

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beniniUC

The Benini Distribution

Description

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

Usage

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 positive 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.

Examples

## 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)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13