Pareto Distribution {extremefit} R Documentation

## Pareto distribution

### Description

Density, distribution function, quantile function and random generation for the Pareto distribution where a, loc and scale are respectively the shape, the location and the scale parameters.

### Usage

```ppareto(q, a = 1, loc = 0, scale = 1)

dpareto(x, a = 1, loc = 0, scale = 1)

qpareto(p, a = 1, loc = 0, scale = 1)

rpareto(n, a = 1, loc = 0, scale = 1)
```

### Arguments

 `q` a vector of quantiles. `a` a vector of shape parameter of the Pareto distribution. `loc` a vector of location parameter of the Pareto distribution. `scale` a vector of scale parameter of the Pareto distribution. `x` a vector of quantiles. `p` a vector of probabilities. `n` a number of observations. If length(n) > 1, the length is taken to be the number required.

### Details

If shape, loc or scale parameters are not specified, the respective default values are 1, 0 and 1.

The cumulative Pareto distribution is

F(x) = 1- ((x-loc)/scale) ^ {-a}, x > loc, a > 0, scale > 0

where a is the shape of the distribution.

The density of the Pareto distribution is

f(x) = (((x-loc)/scale)^( - a - 1) * a/scale) * (x-loc >= scale), x > loc, a > 0, scale > 0

### Value

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

The length of the result is determined by n for rpareto, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

### Examples

```par(mfrow = c(3,1))
plot(function(x) dpareto(x), 1, 5,ylab="density",
main = " Pareto density ")

plot(function(x) ppareto(x), 1, 5,ylab="distribution function",
main = " Pareto Cumulative ")

plot(function(x) qpareto(x), 0, 1,ylab="quantile",
main = " Pareto Quantile ")

#generate a sample of pareto distribution of size n
n <- 100
x <- rpareto(n)

```

[Package extremefit version 1.0.2 Index]