# mle: Maximum Likelihood Estimation of Univariate Probability... In FAmle: Maximum Likelihood and Bayesian 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

 `1` ```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'])`.

`optim`, `distr`, `boot.mle`, `metropolis`, `Q.conf.int`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```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) ```