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

`fitdistr(x, densfun, start, …)`

x

A numeric vector of length at least one containing only finite values.

densfun

Either a character string or a function returning a density evaluated at its first argument.

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.

An object of class `"fitdistr"`

, a list with four components,

the parameter estimates,

the estimated standard errors,

the estimated variance-covariance matrix, and

the log-likelihood.

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"`

.

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

# NOT RUN { ## avoid spurious accuracy op <- options(digits = 3) 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") set.seed(123) x4 <- rnegbin(500, mu = 5, theta = 4) fitdistr(x4, "Negative Binomial") options(op) # }