Computes the confidence interval for the parameter given by param_num using Empirical Likelihood
param_num : float
sig : float
upper_bound : float
lower_bound : float
method : string
ci : tuple
This function uses brentq to find the value of beta where test_beta([beta], param_num) is equal to the critical value.
The function returns the results of each iteration of brentq at each value of beta.
The current function value of the last printed optimization should be the critical value at the desired significance level. For alpha=.05, the value is 3.841459.
To ensure optimization terminated successfully, it is suggested to do el_test([lower_limit], [param_num])
If the optimization does not terminate successfully, consider switching optimization algorithms.
If optimization is still not successful, try changing the values of start_int_params. If the current function value repeatedly jumps from a number between 0 and the critical value and a very large number (>50), the starting parameters of the interior minimization need to be changed.