extremefit (version 1.0.2)

Burr Distribution: 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.

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.

Details

The cumulative Burr distribution is $$ F(x) = 1-( 1 + (x ^ a) ) ^{- k }, x >0, a >0, k > 0 $$

Examples

# NOT RUN {
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)


# }