fitdistr                package:MASS                R Documentation

_M_a_x_i_m_u_m-_l_i_k_e_l_i_h_o_o_d _F_i_t_t_i_n_g _o_f _U_n_i_v_a_r_i_a_t_e _D_i_s_t_r_i_b_u_t_i_o_n_s

_D_e_s_c_r_i_p_t_i_o_n:

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

_U_s_a_g_e:

     fitdistr(x, densfun, start, ...)

_A_r_g_u_m_e_n_t_s:

       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"', '"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. 

_D_e_t_a_i_l_s:

     For the Normal, log-Normal, 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' and 'logLik' methods for class
     '"fitdistr"'.

_V_a_l_u_e:

     An object of class '"fitdistr"', a list with three components,

estimate: the parameter estimates,

      sd: the estimated standard errors, and

  loglik: the log-likelihood.

_R_e_f_e_r_e_n_c_e_s:

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

_E_x_a_m_p_l_e_s:

     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 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") # R only