Beta prime distribution maximum likelihood estimation

This function does not estimate the scale parameter for the BetaPrime distribution. Transforms the data and uses stat::nlm to estimate the parameters of the Beta distribution.

mlbetapr(x, na.rm = FALSE, start = NULL, type = c("none", "gradient",
  "hessian"))

Arguments

x	a (non-empty) numeric vector of data values.
na.rm	logical. Should missing values be removed?
start	Optional starting parameter values for the minimization. Passed to the stats::nlm function.
type	Whether a dedicated gradient or hessian should be passed to stats::nlm.

Value

mlbetapr returns an object of class univariateML. This is a named numeric vector with maximum likelihood estimates for shape1 and shape2 and the following attributes:

model

The name of the model.

density

The density associated with the estimates.

logLik

The loglikelihood at the maximum.

support

The support of the density.

n

The number of observations.

call

The call as captured my match.call

Details

For the density function of the Beta prime distribution see BetaPrime.

For type, the option none is fastest.

References

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, Volume 2, Chapter 25. Wiley, New York.

See also

BetaPrime for the Beta prime density, nlm for the optimizer this function uses, mlbeta for the Beta distribution maximum likelihood estimator.

Examples

AIC(mlbetapr(USArrests$Rape))
#> [1] 363.8231