Sequential Test for a Mixture of Finite Exponential Distribution
Algorithm 1
Put
Step 1: find the MLEs of the parameters of the finite exponential components for and , respectively, by using the code in R.
For
Other
and calculate the LRT statistic, say .
Step 2: declare the initial various variables ,.
Step 3: generate a random sample of size , for the mixture of univariate exponential distributions ,
Step 4: declare the function LRT to calculate ,, and then calculate the LRT by using the EM algorithm equation for finite exponential components, as mentioned in [15].
Step 5: simulate 500 bootstrap samples of size with initial vector parameters ,, and for each bootstrap sample, calculate , for the LRT using the boot package functions in R.
Step 6: find the control variate estimates from a bootstrap output object. Estimate the quantiles using the linear approximation as a control variate.
