Burr Distribution {extremefit} R Documentation

## Burr distribution

### Description

Density, distribution function, quantile function and random generation for the Burr distribution with a and k two parameters.

### Usage

```rburr(n, a, k)

dburr(x, a, k)

pburr(q, a, k)

qburr(p, a, k)
```

### Arguments

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

### Details

The cumulative Burr distribution is

F(x) = 1-( 1 + (x ^ a) ) ^{- k }, x >0, a >0, k > 0

### Value

dburr gives the density, pburr gives the distribution function, qburr gives the quantile function, and rburr generates random deviates.

The length of the result is determined by n for rburr, 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

```plot(function(x) dburr(x,3,1), 0, 5,ylab="density",
main = " burr density ")

plot(function(x) pburr(x,3,1), 0, 5,ylab="distribution function",
main = " burr Cumulative ")

plot(function(x) qburr(x,3,1), 0, 1,ylab="quantile",
main = " burr Quantile ")

#generate a sample of burr distribution of size n
n <- 100
x <- rburr(n, 1, 1)

```

[Package extremefit version 1.0.2 Index]