mle: Maximum Likelihood Estimation of Univariate Probability...

In FAmle: Maximum Likelihood and Bayesian Estimation of Univariate Probability Distributions

Maximum Likelihood Estimation of Univariate Probability Distributions

Description

For a given dataset, this function serves to find maximum likelihood parameter estimates for some specified parametric probability distribution.

Usage

mle(x, dist, start = NULL, method = "Nelder-Mead")

Arguments

x	A univariate dataset (a vector).
dist	Distribution to be fitted to x.
start	Starting parameter values for the optimization algorithm (see optim).
method	The optimization method to be used (see optim).

Value

fit	optim output (see optim).
x.info	Array that contains the following columns: i: (1:length(x)), x: (original dataset), z: (sorted dataset), Fx: (CDF of x evaluated at the estimated parameter values), Fz: (sorted values of Fx), Emp: (i/(length(x)+1)), zF: (distr(Emp,'dist',par.hat,'q') evaluated at estimated parameter values (par.hat)), fx: (PDF of x evaluated at the estimated parameter values), fz: (PDF of z evaluated at the estimated parameter values)
dist	Distribution fitted to x.
par.hat	Vector of estiamted parameters.
cov.hat	Observed Fisher's information matrix.
k	Number of parameters
n	Number of observations (i.e., length(x)).
log.like	Log-likelihood value evaluated at the estimated parameter (i.e. par.hat).
aic	Akaike information criterion computed as 2*k - 2*log.like.
ad	Anderson Darling statistic evaluated at the estimated parameter values.
data.name	Name for x.
rho	Pearson's correlation coefficient computed as cor(x.info[,'z'],x.info[,'zF']).

See Also

optim, distr, boot.mle, metropolis, Q.conf.int

Examples

data(yarns)
x <- yarns$x
fit.x <- mle(x,'weibull',c(.1,.1))
fit.x
names(fit.x)
#plot(fit.x)
#plot(fit.x,TRUE,alpha=.01)
p <- c(.9,.95,.99)
distr(p,model=fit.x,type='q')
Q.conf.int(p,fit.x,.01)
Q.conf.int(p,fit.x,.01,TRUE)

FAmle documentation built on March 18, 2022, 5:29 p.m.