Examples
| Distribution | Characteristic function φ(t) |
|---|---|
| Degenerate δa | |
| Bernoulli Bern(p) | |
| Binomial B(n, p) | |
| Negative binomial NB(r, p) | |
| Poisson Pois(λ) | |
| Uniform U(a, b) | |
| Laplace L(μ, b) | |
| Normal N(μ, σ2) | |
| Chi-squared χ2k | |
| Cauchy C(μ, θ) | |
| Gamma Γ(k, θ) | |
| Exponential Exp(λ) | |
| Multivariate normal N(μ, Σ) | |
| Multivariate Cauchy MultiCauchy(μ, Σ) |
Oberhettinger (1973) provides extensive tables of characteristic functions.
Read more about this topic: Characteristic Function (probability Theory)
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