# pmle.exp: compute the PMLE or MLE of the parameters under a mixture of... In MixtureInf: Inference for Finite Mixture Models

## Description

Compute the PMLE or MLE of the parameters under a mixture of exponentials. When the level of penalty is 0, PMLE reduces to MLE.

## Usage

 ```1 2``` ```pmle.exp(x, m0 = 1, lambda = 0, inival = NULL, len = 10, niter = 50, tol = 1e-06, rformat = FALSE) ```

## Arguments

 `x` data, can be either a vector or a matrix with the 1st column being the observed values and the 2nd column being the corresponding frequencies. `m0` order of the finite mixture model, default value: m0 = 1. `lambda` level of penalty, default value: lambda = 0. `inival` initial values for the EM-algorithm, a 2m0-dimension vector including m0 mixing proportions and m0 component parameters, or a matrix with 2m0 columns, default value: inival = NULL. (if not provided, random initial values are used.) `len` number of random initial values for the EM-algorithm, default value: len = 10. `niter` number of iterations for all initial values in the EM-algorithm. The algorithm runs EM-iteration niter times from each initial value. The iteration will restart from the parameter value with the highest likelihood value at the point and run until convergence. default value: niter = 50. `tol` tolerance level for the convergence of the EM-algorithm, default value: tol = 1e-6. `rformat` form of the digital output: default of R package is used when rformat = T; If rformat = T, the digital output is rounded to the 3rd dicimal place if it is larger than 0.001, keeps 3 significant digits otherwise. The default value of rformat is F.

## Value

Return the PMLE or MLE of the parameters with order = m0 (mixing proportions and component parameters), log-likelihood value at the PMLE or MLE and the penalized log-likelihood value at the PMLE.

## Author(s)

Shaoting Li, Jiahua Chen and Pengfei Li

 ```1 2 3 4 5 6``` ```#generate a random sample from a 2 component exponential mixture, #compute the PMLE of the parameters under 2 component exponential mixture model, #plot the histgoram of the observations and the fitted density. x <- rmix.exp(200,c(0.3,0.7),c(2,8)) out <- pmle.exp(x,2,1) plotmix.exp(x,out) ```