Bird’s Eye View to Indonesian Mass Conflict Revisiting the Fact of Self-Organized Criticality

consequently, p(x)dx denotes the fraction of the conflict event with casualties in the
interval of [x,x + dx]. Thus, we can write down the cumulative distribution function - as the
probability of a certain statistical event in the death toll of which certain number of victims
equals to or greater than x - that also follows the power law

∞

P(x)=∫ p(x')dx'=

x

However, we understood that not all of the data in the data distribution fulfills the power-
law (Newman, 2005). By observing the equation (2) above, we understood that in the
cumulative distribution function, there would be such x_min that would make the distribution
of the data become able to be normalized as,

and this become the main reason for the power laws would generally fulfils α> 1 .
Apparently, the value of xmin is not necessarily the minimum number in our data set but the
minimum value for the data fulfils the power law. Hence, we have the normalized
expression of for the power law becomes

In our fitting processes to the distribution of the data, we use the value of Xmin = 9.9623 that
is the value with which the data x ≥ x_min comply the power law.

Furthermore, as we always fit the power-law distributed data better in the
logarithmic axes, usually we found the data fluctuates in large values in the tail of the
distribution. In order to avoid the difficulties may arise in the fitting process, we reduce the
fluctuation by using the logarithmic binning so that bins of the data span at increasingly
larger intervals exponentially (eⁱ where i denotes the iterative numbers).

In our analysis we use two methods of fitting processes. The first is the maximum
likelihood estimator (MLE) as introduced and derived in Newman (2005),
where n is the number of the data, and xmin the practical minimum value for the data points
xi follows the power law as discussed previously. Furthermore, the estimate of the expected
statistical error σ is given by

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