Laplace Distribution

Tags: #Math #Statistics

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

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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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