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We analytically estimate the risk function of natural hazards (earthquakes, rockfalls, forestfires, landslides) by means of a non-extensive approach which is based on implementing the Tsallis entropy for the estimation of the probability density function (PDF) and introducing a phenomenological exponential expression for the damage function. The result leads to a power law expression as a special case and the b-value is given as a function of the non-extensive parameter <i>q</i>. A discussion of risk function dependence on the parameters of hazard PDF and damage function for various hazards is given.