# boot.mle: Bootstrap Distribution for Fitted Model In FAmle: Maximum Likelihood and Bayesian Estimation of Univariate Probability Distributions

## Description

This function allows the user to obtain draws from the (parametric) bootstrap distribution of the fitted model's parameters.

## Usage

 ```1 2``` ```boot.mle(model, B = 200, seed = NULL, start = NULL, method = "Nelder-Mead") ```

## Arguments

 `model` `mle` object corresponding to the fitted model. `B` Requested number of bootstrap samples. `seed` A seed may be specified (see `set.seed`) `start` Starting values for the optimization algorithm (if `is.null(start)==TRUE`, the fitted model's parameters are used as starting values). `method` The optimization method to be used (see `optim` and `mle`).

## Details

Parametric bootstrap – see References.

## Value

 `model` `mle` object corresponding to the fitted model. `B` Requested number of bootstrap samples. `seed` The specified seed (see `set.seed`) `par.star` Array containing realized values from the bootstrap distribution of the maximum likelihood parameter estimators. `gof` The bootstrap distributions of two goodness-of-fit statistics: Anderson-Darling statistic and Pearson's correlation coefficient for the pair ("observed quantiles","fitted quantiles"). `p.value` Bootstrap p-values for the two goodness-of-fit statistics. `failure.rate` The proportion of bootstrap samples for which optimization failed using the specified starting values. `total.time` The total amount of time required to generate `B` bootstrap samples.

## References

Davison, A.C., and Hinkley, D.V. (1997). Bootstrap methods and their application. Cambridge University Press.

`mle`, `Q.conf.int`, `Q.boot.ci`
 ```1 2 3 4 5 6``` ```data(yarns) x <- yarns\$x fit.x <- mle(x,'weibull',c(.1,.1)) boot.x <- boot.mle(fit.x,B=10) boot.x\$par.star boot.x\$p.value ```