Density, distribution function, quantile function, random generation and calculation of the expected value for the Burr distribution with parameters theta, kappa and sig2.
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)
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.
vector of quantiles.
vector of probabilities.
number of observations..
parameters, see 'Details'.
logical; if TRUE, the expectation of the distribution is forced to be 1 by letting theta be a function of the other parameters.
Markus Belfrage
The PDF for the Burr distribution is (as in e.g. Grammig and Maurer, 2000): $$f(x)=\frac{\theta \kappa x^{\kappa - 1}}{(1 + \sigma^2 x^{\kappa)^{\frac{1}{\sigma^2}+1}}}$$
Grammig, J., and Maurer, K.-O. (2000) Non-monotonic hazard functions and the autoregressive conditional duration model. Econometrics Journal 3: 16-38.