fitdistr {MASS} | R Documentation |

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 |

`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 |

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"`

.

An object of class `"fitdistr"`

, a list with four components,

`estimate` |
the parameter estimates, |

`sd` |
the estimated standard errors, |

`vcov` |
the estimated variance-covariance matrix, and |

`loglik` |
the log-likelihood. |

Numerical optimization cannot work miracles: please note the comments
in `optim`

on scaling data. If the fitted parameters are
far away from one, consider re-fitting specifying the control
parameter `parscale`

.

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

## 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)

[Package *MASS* version 7.3-23 Index]