Exponential Distribution
Exponential Distribution#
The exponential distribution is a single-parameter continuous probability distribution.
The table below summarizes some important aspects of the distribution.
Notation |
\(X \sim \mathcal{E}(\lambda)\) |
Parameters |
\(\lambda \in \mathbb{R}_{>0}\) (rate parameter) |
\(\mathcal{D}_X = [0.0, \infty)\) |
|
\(f_X (x; \lambda) = \lambda e^{-\lambda x}\) |
|
\(F_X (x; \lambda) = 1 - e^{-\lambda x}\) |
|
\(F^{-1}_X (x; \lambda) = - \frac{1}{\lambda} \ln{(1 - x)}\) |
The plots of probability density functions (PDFs), sample histogram (of \(5'000\) points), cumulative distribution functions (CDFs), and inverse cumulative distribution functions (ICDFs) for different parameter values are shown below.
