The Pareto distribution is a continuous probability distribution that models situations where a small number of events account for a large proportion of the outcome. It is characterized by a power-law shape and is often used to describe phenomena involving inequality or imbalance. The Pareto distribution is right-skewed and has a heavy tail, meaning it predicts a non-negligible probability of very large values. Analysts frequently use it in economics (wealth distribution), insurance (large claims), and internet traffic (file sizes).
The Pareto distribution is defined by two parameters:
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xₘ: the minimum possible value (scale parameter)
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α (alpha): the shape parameter, which determines the heaviness of the tail
For example, in modeling income or wealth, the Pareto distribution reflects the idea that a small percentage of individuals hold the majority of the wealth. With a shape parameter of α = 2.5, the distribution shows how likely it is to observe individuals with higher and higher wealth levels, starting from a minimum threshold.
The graph below shows a Pareto distribution modeling wealth, starting at a minimum value of 1. The steep drop from the peak shows that most people have modest wealth, while the long, gradually declining tail shows that a few individuals hold much greater wealth levels. This pattern aligns with real-world income distributions where large values are rare but impactful. The heavier the tail (lower α), the more concentrated the outcome becomes among the few.
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