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. 2017 Mar 21;7:273. doi: 10.1038/s41598-017-00253-1

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© The Author(s) 2017

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Maximum log-likelihood (MLL) as a function of reporting ratio ρ for (a) French Polynesia, ρ _f; (b) Colombia, ρ _c; and (c) the State of Bahia in Brazil, ρ _b, respectively. The red circles denote the estimated MLL at the given value of the control parameter. The black curves denote Local Polynomial Regression Fittings with a span of 0.5. The blue dotted lines indicate the thresholds of − $\frac{1}{2} χ_{0.95,1}^{2}$ from the maximum of the MLL. The maximum value of the black curve gives the maximum log-likelihood estimate of the control parameter, while the intersections of the two curves yield the 95% CI.