The Fisk Distribution

Density, distribution function, quantile function and random generation for the Fisk distribution with shape parameter a and scale parameter scale.

Usage

dfisk(x, scale = 1, shape1.a, log = FALSE)
pfisk(q, scale = 1, shape1.a, lower.tail = TRUE, log.p = FALSE)
qfisk(p, scale = 1, shape1.a, lower.tail = TRUE, log.p = FALSE)
rfisk(n, scale = 1, shape1.a)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1 then the length is taken to be the number required.

shape1.a

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

dfisk gives the density, pfisk gives the distribution function, qfisk gives the quantile function, and rfisk 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 and Kai Huang

Details

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

Note

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

See also

fisk, genbetaII.

Examples

fdata <- data.frame(y = rfisk(1000, shape = exp(1), scale = exp(2)))
fit <- vglm(y ~ 1, fisk(lss = FALSE), data = fdata, trace = TRUE)
#> Iteration 1: loglikelihood = -2998.765
#> Iteration 2: loglikelihood = -2998.7635
#> Iteration 3: loglikelihood = -2998.7635
coef(fit, matrix = TRUE)
#>             loglink(shape1.a) loglink(scale)
#> (Intercept)         0.9760154       1.978601
Coef(fit)
#> shape1.a    scale 
#> 2.653860 7.232616