The Laplace distribution is a continuous probability distribution that resembles the normal distribution but with a sharper peak at the center and heavier tails. Statisticians also refer to it as the double exponential distribution due to its characteristic exponential decay on both sides of the mean. The Laplace distribution is symmetric and useful for modeling data with a large concentration of values near the mean, but also with a higher likelihood of large deviations than the normal distribution would suggest. Analysts commonly use it in signal processing, finance, and Bayesian estimation, particularly when dealing with sharp jumps or sudden changes.
The Laplace distribution is defined by two parameters:
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μ (mu): the location parameter, which sets the center
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b: the scale parameter, sometimes called the diversity, which controls the spread
For example, financial analysts may use a Laplace distribution to model daily percentage price changes in a stock that tends to be stable but occasionally experiences large, sudden moves due to market shocks or news.
The graph below shows a Laplace distribution centered at 0, representing no price change. The sharp central peak reflects that most days have small price changes, while the heavy tails indicate that large jumps—either positive or negative—are more likely than they would be under a normal distribution. This makes the Laplace distribution well-suited for modeling systems with both stability and occasional volatility.
