R: Pre-fitting procedure

prefit {fitdistrplus} | R Documentation

## Pre-fitting procedure

### Description

Search good starting values

### Usage

    prefit(data, distr, method = c("mle", "mme", "qme", "mge"),
      feasible.par, memp=NULL, order=NULL,
      probs=NULL, qtype=7, gof=NULL, fix.arg=NULL, lower,
      upper, weights=NULL, silent=TRUE, ...)

### Arguments

`data` | A numeric vector.
`distr` | A character string `"name"` naming a distribution for which the corresponding density function `dname`, the corresponding distribution function `pname` and the corresponding quantile function `qname` must be defined, or directly the density function.
`method` | A character string coding for the fitting method: `"mle"` for 'maximum likelihood estimation', `"mme"` for 'moment matching estimation', `"qme"` for 'quantile matching estimation' and `"mge"` for 'maximum goodness-of-fit estimation'.
`feasible.par` | A named list giving the initial values of parameters of the named distribution or a function of data computing initial values and returning a named list. This argument may be omitted (default) for some distributions for which reasonable starting values are computed (see the 'details' section of `mledist`). It may not be into account for closed-form formulas.
`order` | A numeric vector for the moment order(s). The length of this vector must be equal to the number of parameters to estimate.
`memp` | A function implementing empirical moments, raw or centered but has to be consistent with `distr` argument (and `weights` argument).
`probs` | A numeric vector of the probabilities for which the quantile matching is done. The length of this vector must be equal to the number of parameters to estimate.
`qtype` | The quantile type used by the R `quantile` function to compute the empirical quantiles, (default 7 corresponds to the default quantile method in R).
`gof` | A character string coding for the name of the goodness-of-fit distance used : "CvM" for Cramer-von Mises distance,"KS" for Kolmogorov-Smirnov distance, "AD" for Anderson-Darling distance, "ADR", "ADL", "AD2R", "AD2L" and "AD2" for variants of Anderson-Darling distance described by Luceno (2006).
`fix.arg` | An optional named list giving the values of fixed parameters of the named distribution or a function of data computing (fixed) parameter values and returning a named list. Parameters with fixed value are thus NOT estimated by this maximum likelihood procedure. The use of this argument is not possible if `method="mme"` and a closed-form formula is used.
`weights` | an optional vector of weights to be used in the fitting process. Should be `NULL` or a numeric vector. If non-`NULL`, weighted MLE is used, otherwise ordinary MLE.
`silent` | A logical to remove or show warnings.
`lower` | Lower bounds on the parameters.
`upper` | Upper bounds on the parameters.
`...` | Further arguments to be passed to generic functions, or to one of the functions `"mledist"`, `"mmedist"`, `"qmedist"` or `"mgedist"` depending of the chosen method. See `mledist`, `mmedist`, `qmedist`, `mgedist` for details on parameter estimation.

### Details

Searching good starting values is achieved by transforming the parameters (from their constraint interval to the real line) of the probability distribution. Indeed,

- positive parameters in (0,Inf) are transformed using the logarithm (typically the scale parameter `sd` of a normal distribution, see Normal),

- parameters in (1,Inf) are transformed using the function log(x-1),

- probability parameters in (0,1) are transformed using the logit function log(x/(1-x)) (typically the parameter `prob` of a geometric distribution, see Geometric),

- negative probability parameters in (-1,0) are transformed using the function log(-x/(1+x)),

- real parameters are of course not transformed at all, typically the `mean` of a normal distribution, see Normal.

Once parameters are transformed, an optimization is carried out by a quasi-Newton algorithm (typically BFGS) and then we transform them back to original parameter value.

### Value

A named list.

### Author(s)

Christophe Dutang and Marie-Laure Delignette-Muller.

### References

Delignette-Muller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1-34.

### See Also

See `mledist`, `mmedist`, `qmedist`, `mgedist` for details on parameter estimation. See `fitdist` for the main procedure.

### Examples

    # (1) fit of a gamma distribution by maximum likelihood estimation
    #
    x <- rgamma(1e3, 5/2, 7/2)

    prefit(x, "gamma", "mle", list(shape=3, scale=3), lower=-Inf, upper=Inf)

[Package fitdistrplus version 1.0-9 Index]