distfit: Maximum-Likelihood Fitting of Parametric Distributions

In disttree: Trees and Forests for Distributional Regression

Description

The function distfit carries out maximum-likelihood estimation of parameters for a specified distribution family, for example from the GAMLSS family (for generalized additive models for location, scale, and shape). The parameters can be transformed through link functions but do not depend on further covariates (i.e., are constant across observations).

Usage

distfit(y, family = NO(), weights = NULL, start = NULL, start.eta = NULL,
          vcov = TRUE, type.hessian =  c("checklist", "analytic", "numeric"),
          method = "L-BFGS-B", estfun = TRUE, optim.control = list(), ...)

Arguments

y	numeric vector of the response
family	specification of the response distribution. Either a gamlss.family object, a list generating function or a family list.
weights	optional numeric vector of case weights.
start	starting values for the distribution parameters handed over to optim
start.eta	starting values for the distribution parameters on the link scale handed over to optim.
vcov	logical. Specifies whether or not a variance-covariance matrix should be calculated and returned.
type.hessian	Can either be 'checklist', 'analytic' or 'numeric' to decide how the hessian matrix should be calculated in the fitting process in distfit. For 'checklist' it is checked whether a function 'hdist' is given in the family list. If so, 'type.hessian' is set to 'analytic', otherwise to 'numeric'.
method	Optimization which should be applied in optim
estfun	logical. Should the matrix of observation-wise score contributions (or empirical estimating functions) be returned?
optim.control	A list with optim control parameters.
...	further arguments passed to optim.

Details

The function distfit fits distributions, similar to fitdistr from MASS (Venables and Ripley 2002) but based on GAMLSS families (Stasinopoulos and Rigby 2007).

Provides analytical gradients and hessian, can be plugged into mob.

The resulting object of class distfit comes with a set of standard methods to generic functions including coef, estfun, vcov, predict and logLik.

Value

distfit returns an object of class distfit which is a list with the following components:

npar	number of parameter
y	numeric vector of the response
ny	number of observations
weights	numeric vector of case weights handed over as input argument
family	employed distribution family list of class disttree.family
start	used starting values in optim that were handed over as input argument
starteta	starting values on the link scale used in optim
opt	list returned by optim
converged	logical. TRUE if optim returns convergence = 0 and FALSE else.
par	fitted distribution parameters (on parameter scale)
eta	fitted distribution parameters (on link scale)
hess	hessian matrix
vcov	variance-covariance matrix
loglik	value of the maximized log-likelihood function
call	function call
estfun	matrix with the scores for the estimated parameters. Each line represents an observation and each column a parameter.
ddist	density function with the estimated distribution parameters already plugged in
pdist	probability function with the estimated distribution parameters already plugged in
qdist	quantile function with the estimated distribution parameters already plugged in
rdist	random number generating function with the estimated distribution parameters already plugged in
method	optimization method applied in optim

References

Stasinopoulos DM, Rigby RA (2007). Generalized Additive Models for Location Scale and Shape (GAMLSS) in R, Journal of Statistical Software, 23(7), 1-46. doi: 10.18637/jss.v023.i07

Venables WN, Ripley BD (2002). Modern Applied Statistics with S. 4th Edition. Springer-Verlag, New York.

See Also

gamlss.family, optim

Examples

## simulate artifical negative binomial data
set.seed(0)
y <- rnbinom(1000, size = 1, mu = 2)
  
## simple distfit
df <- distfit(y, family = NBI)

disttree documentation built on Aug. 14, 2019, 3 a.m.