fitdistr {MASS}R Documentation

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.
densfun Either a character string or a function returning a density evaluated at its first argument.
Distributions "beta", "cauchy", "chi-squared", "exponential", "f", "gamma", "log-normal", "lognormal", "logistic", "negative binomial", "normal", "t", "uniform" 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 (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 densfun = "normal" the closed-form MLEs (and standard errors) are used, and start should not be supplied.

For all other distributions, direct optimization of the log-likelihood is performed, with numerical derivatives. The estimated standard errors are taken from the observed information matrix, calculated by a numerical approximation.

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, uniform, weibull.

Value

An object of class "fitdistr", a list with two components,

estimate the parameter estimates, and
sd the estimated standard errors.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

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 = 0.01)

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 this 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")

set.seed(123)
x4 <- rnegbin(500, mu = 5, theta = 4)
fitdistr(x4, "Negative Binomial") # R only
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