FitDistr: FitDistr: Maximum-likelihood Fitting of Univariate...

In r6qualitytools: R6-Based Statistical Methods for Quality Science

FitDistr: Maximum-likelihood Fitting of Univariate Distributions

Description

Maximum-likelihood fitting of univariate distributions, allowing parameters to be held fixed if desired.

Usage

FitDistr(x, densfun, start, ...)

Arguments

x	A numeric vector of length at least one containing only finite values. Either a character string or a function returning a density evaluated at its first argument.
densfun	character string specifying the density function to be used for fitting the distribution. Distributions '"beta"', '"cauchy"', '"chi-squared"', '"exponential"', '"gamma"', '"geometric"', '"log-normal"', '"lognormal"', '"logistic"', '"negative binomial"', '"normal"', '"Poisson"', '"t"' and "weibull" are recognised, case being ignored.
start	A named list giving the parameters to be optimized with initial values. This can be omitted for some of the named distributions and must be for others (see Details).
...	Additional parameters, either for 'densfun' or for 'optim'. In particular, it can be used to specify bounds via 'lower' or 'upper' or both. If arguments of 'densfun' (or the density function corresponding to a character-string specification) are included they will be held fixed.

Details

For the Normal, log-Normal, geometric, exponential and Poisson distributions the closed-form MLEs (and exact standard errors) are used, and 'start' should not be supplied.

For all other distributions, direct optimization of the log-likelihood is performed using 'optim'. The estimated standard errors are taken from the observed information matrix, calculated by a numerical approximation. For one-dimensional problems the Nelder-Mead method is used and for multi-dimensional problems the BFGS method, unless arguments named 'lower' or 'upper' are supplied (when 'L-BFGS-B' is used) or 'method' is supplied explicitly.

For the '"t"' named distribution the density is taken to be the location-scale family with location 'm' and scale 's'.

For the following named distributions, reasonable starting values will be computed if 'start' is omitted or only partially specified: '"cauchy"', '"gamma"', '"logistic"', '"negative binomial"' (parametrized by mu and size), '"t"' and '"weibull"'. Note that these starting values may not be good enough if the fit is poor: in particular they are not resistant to outliers unless the fitted distribution is long-tailed.

There are 'print', 'coef', 'vcov' and 'logLik' methods for class '"FitDistr"'.

Value

The function 'FitDistr' returns an object of class 'fitdistr', which is a list containing:

estimate	a named vector of parameter estimates.
sd	a named vector of the estimated standard errors for the parameters.
vcov	the estimated variance-covariance matrix of the parameter estimates.
loglik	the log-likelihood of the fitted model.
n	length vector.

See Also

distribution, Distr, DistrCollection.

Examples

set.seed(123)
x = rgamma(100, shape = 5, rate = 0.1)
FitDistr(x, "gamma")

# Now do this directly with more control.
FitDistr(x, dgamma, list(shape = 1, rate = 0.1), lower = 0.001)

set.seed(123)
x2 = rt(250, df = 9)
FitDistr(x2, "t", df = 9)

# Allow df to vary: not a very good idea!
FitDistr(x2, "t")

# Now do fixed-df fit directly with more control.
mydt = function(x, m, s, df) dt((x-m)/s, df)/s
FitDistr(x2, mydt, list(m = 0, s = 1), df = 9, lower = c(-Inf, 0))

set.seed(123)
x3 = rweibull(100, shape = 4, scale = 100)
FitDistr(x3, "weibull")

r6qualitytools documentation built on Oct. 4, 2024, 1:09 a.m.