ACDm (version 1.0.3)

BurrDist: 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.

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.

Details

The PDF for the Burr distribution is (as in e.g. Grammig and Maurer, 2000): $$f(x)=\frac{\theta \kappa x^{\kappa - 1}}{(1 + \sigma^2 x^{\kappa)^{\frac{1}{\sigma^2}+1}}}$$

References

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