BurrDist {ACDm} R Documentation

## The Burr Distribution

### Description

Density, distribution function, quantile function, random generation and calculation of the expected value for the Burr distribution with parameters theta, kappa and sig2.

### Usage

dburr(x, theta = 1, kappa = 1.2, sig2 = 0.3, forceExpectation = F)
pburr(x, theta = 1, kappa = 1.2, sig2 = .3, forceExpectation = F)
qburr(p, theta = 1, kappa = 1.2, sig2 = .3, forceExpectation = F)
rburr(n = 1, theta = 1, kappa = 1.2, sig2 = .3, forceExpectation = F)
burrExpectation(theta = 1, kappa = 1.2, sig2 = .3)


### Arguments

 x vector of quantiles. p vector of probabilities. n number of observations.. theta, kappa, sig2 parameters, see 'Details'. forceExpectation logical; if TRUE, the expectation of the distribution is forced to be 1 by letting theta be a function of the other parameters.

### Details

The PDF for the Burr distribution is (as in e.g. Grammig and Maurer, 2000):

f(x)=\frac{θ κ x^{κ - 1}}{(1 + σ^2 x^{κ)^{\frac{1}{σ^2}+1}}}

### Value

dburr gives the density (PDF), qburr the quantile function (inverted CDF), rburr generates random deviates, and burrExpectation returns the expected value of the distribution, given the parameters.

Markus Belfrage

### References

Grammig, J., and Maurer, K.-O. (2000) Non-monotonic hazard functions and the autoregressive conditional duration model. Econometrics Journal 3: 16-38.

[Package ACDm version 1.0.4 Index]