Pareto {VGAM} R Documentation

## The Pareto Distribution

### Description

Density, distribution function, quantile function and random generation for the Pareto(I) distribution with parameters `location` and `shape`.

### Usage

```dpareto(x, location, shape)
ppareto(q, location, shape)
qpareto(p, location, shape)
rpareto(n, location, shape)
```

### Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of observations. Must be a single positive integer. `location, shape` the alpha and k parameters.

### Details

See `pareto1`, the VGAM family function for estimating the parameter k by maximum likelihood estimation, for the formula of the probability density function and the range restrictions imposed on the parameters.

### Value

`dpareto` gives the density, `ppareto` gives the distribution function, `qpareto` gives the quantile function, and `rpareto` generates random deviates.

T. W. Yee

### References

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

`pareto1`, `ParetoIV`.

### Examples

```alpha = 3; k = exp(1); x = seq(2.8, 8, len=300)
## Not run:
plot(x, dpareto(x, location=alpha, shape=k), type="l",
main="Pareto density split into 10 equal areas")
abline(h=0, col="blue", lty=2)
qq = qpareto(seq(0.1,0.9,by=0.1),location=alpha,shape=k)
lines(qq, dpareto(qq, loc=alpha, shape=k), col="purple", lty=3, type="h")
## End(Not run)
pp = seq(0.1,0.9,by=0.1)
qq = qpareto(pp, location=alpha, shape=k)
ppareto(qq, location=alpha, shape=k)
qpareto(ppareto(qq,loc=alpha,shape=k),loc=alpha,shape=k) - qq # Should be 0
```

[Package VGAM version 0.7-7 Index]