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"', '"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. 

_D_e_t_a_i_l_s:

     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'.

_V_a_l_u_e:

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

estimate: the parameter estimates, and

      sd: the estimated standard errors.

_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 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

