What the documentation page you linked to means to say is that the new keyword only exists within inner constructors (as opposed to outer constructors).
So either you go for an outer constructor, in which case you want to use the default constructor in order to actually create your new instance:
using Statistics
# First the type declaration, which comes with a default constructor
struct NormalDistribution{P}
mu::Float64
sigma::Float64
pdf::P
end
# Another outer constructor
function NormalDistribution(x::Array)
μ = mean(x)
σ = std(x)
pdf(xt::Array) = [(i-μ) / σ for i in xt]
# This is a call to the constructor that was created for you by default
return NormalDistribution(μ, σ, pdf)
end
julia> x = [5, 10, 15, 20]
4-element Array{Int64,1}:
5
10
15
20
julia> dist = NormalDistribution(x)
NormalDistribution{var"#pdf#2"{Float64,Float64}}(12.5, 6.454972243679028, var"#pdf#2"{Float64,Float64}(12.5, 6.454972243679028))
julia> dist.pdf([1, 2, 3])
3-element Array{Float64,1}:
-1.781572339255412
-1.626653005407115
-1.4717336715588185
Note that the definition of pdf in the original article is obviously problematic (if only because μ and σ are not defined). I tried to modify it so that it makes some sense
One possible issue with this is that anyone can define a NormalDistribution instance with an inconsistent state:
julia> NormalDistribution(0., 1., x->x+1)
NormalDistribution{var"#11#12"}(0.0, 1.0, var"#11#12"())
Which is why you might want to actually define an inner constructor, in which case Julia does not provide you with a default constructor but you get access to that special new function which creates objects of the type you're defining:
# A type declaration with an inner constructor
struct NormalDistribution2{P}
mu::Float64
sigma::Float64
pdf::P
# The inner constructor is defined inside the type declaration block
function NormalDistribution2(x::Array)
μ = mean(x)
σ = std(x)
pdf(xt::Array) = [(i-μ) / σ for i in xt]
# Use the `new` function to actually create the object
return new{typeof(pdf)}(μ, σ, pdf)
end
end
It behaves exactly in the same way as the struct with an outer constructor, except this time no default constructor is provided anymore:
julia> dist2 = NormalDistribution2(x)
NormalDistribution2{var"#pdf#5"{Float64,Float64}}(12.5, 6.454972243679028, var"#pdf#5"{Float64,Float64}(12.5, 6.454972243679028))
julia> dist2.pdf([1, 2, 3])
3-element Array{Float64,1}:
-1.781572339255412
-1.626653005407115
-1.4717336715588185
# No default constructor provided
julia> NormalDistribution2(0., 1., x->x+1)
ERROR: MethodError: no method matching NormalDistribution2(::Float64, ::Float64, ::var"#9#10")
Stacktrace:
[1] top-level scope at REPL[13]:1