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Update erlang.jl docstring #1915

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Update erlang.jl docstring #1915

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2851fc3
Update erlang.jl docstring
theplatters Nov 14, 2024
900584b
Update erlang.jl docstring to be consistent with gamma.jl
theplatters Nov 14, 2024
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11 changes: 8 additions & 3 deletions src/univariate/continuous/erlang.jl
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Original file line number Diff line number Diff line change
@@ -1,12 +1,17 @@
"""
Erlang(α,θ)
Erlang(α=1,θ=1)

The *Erlang distribution* is a special case of a [`Gamma`](@ref) distribution with integer shape parameter.
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The *Erlang distribution* is a special case of a [`Gamma`](@ref) distribution with integer shape parameter.
The *Erlang distribution* is a special case of a [`Gamma`](@ref) distribution with integer shape parameter α and scale parameter θ.


```math
f(x; α, θ) = \\frac{x^{α-1} e^{-x/ θ}}{(α-1)! θ^a},
\\quad x > 0
```

```julia
Erlang() # Erlang distribution with unit shape and unit scale, i.e. Erlang(1, 1)
Erlang(a) # Erlang distribution with shape parameter a and unit scale, i.e. Erlang(a, 1)
Erlang(a, s) # Erlang distribution with shape parameter a and scale s
Erlang(α) # Erlang distribution with shape parameter a and unit scale, i.e. Erlang(a, 1)
Erlang(α, θ) # Erlang distribution with shape parameter a and scale s
```

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