code: private double likelihoodRatio(int c1, int c2, int c12, long N) {
          double p = (double) c2 / N;
          double p1 = (double) c12 / c1;
          double p2 = (double) (c2 - c12) / (N - c1);
  
          double logLambda = logL(c12, c1, p) + logL(c2-c12, N-c1, p) - logL(c12, c1, p1) - logL(c2-c12, N-c1, p2);
          return -2 * logLambda;
      }
docs: Returns the likelihood ratio test statistic -2 log &lambda;
  @param c1 the number of occurrences of w1.
  @param c2 the number of occurrences of w2.
  @param c12 the number of occurrences of w1 w2.
  @param N the number of tokens in the corpus.