Laplace Distribution
Tags: #Math #StatisticsEquation
$$x \sim \text{Laplace}(\mu,b), \\ f(x | \mu,b) =\frac{1}{2b} \exp (-\frac{|x-\mu|}{b}), \\ F(x | \mu,b) = \frac{1}{2} \exp (\frac{x - \mu}{b}) \text{ if } x \le \mu, 1 - \frac{1}{2} \exp (-\frac{x - \mu}{b}) \text{ if } x \ge \mu$$Latex Code
x \sim \text{Laplace}(\mu,b), \\
f(x | \mu,b) =\frac{1}{2b} \exp (-\frac{|x-\mu|}{b}), \\
F(x | \mu,b) = \frac{1}{2} \exp (\frac{x - \mu}{b}) \text{ if } x \le \mu, 1 - \frac{1}{2} \exp (-\frac{x - \mu}{b}) \text{ if } x \ge \mu
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Introduction
Equation
$$x \sim \text{Laplace}(\mu,b)$$ $$f(x | \mu,b) =\frac{1}{2b} \exp (-\frac{|x-\mu|}{b})$$ $$F(x | \mu,b) = \frac{1}{2} \exp (\frac{x - \mu}{b}) \text{ if } x \le \mu, 1 - \frac{1}{2} \exp (-\frac{x - \mu}{b}) \text{ if } x \ge \mu$$
Latex Code
x \sim \text{Laplace}(\mu,b), \\
f(x | \mu,b) =\frac{1}{2b} \exp (-\frac{|x-\mu|}{b}), \\
F(x | \mu,b) = \frac{1}{2} \exp (\frac{x - \mu}{b}) \text{ if } x \le \mu, 1 - \frac{1}{2} \exp (-\frac{x - \mu}{b}) \text{ if } x \ge \mu
Explanation
Latex code for Laplace Distribution. Laplace Distribution is also called double exponential distribution. It can be thought of as two exponential distributions spliced together. \mu denotes the location parameters and b is the scale parameter.
- PDF of Laplace Distribution: $$f(x | \mu,b) =\frac{1}{2b} \exp (-\frac{|x-\mu|}{b})$$
- CDF of Laplace Distribution: $$F(x | \mu,b) = \frac{1}{2} \exp (\frac{x - \mu}{b}) \text{ if } x \le \mu, 1 - \frac{1}{2} \exp (-\frac{x - \mu}{b}) \text{ if } x \ge \mu$$
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