feat: cumulative mean & var

src/estimate_statistics.jl

@@ -233,9 +233,41 @@ function scv(u::AbstractArray{T,N}; dims=:) where {T,N}
 end
 
 function cumscv(u::AbstractArray{T,N}; dims=N) where {T,N}
+    sz = ntuple(i -> i == dims ? size(u, dims) : 1, N)
+
     I = abs2.(u)
     I² = I .^ 2
-    cumsum(I²; dims) .* (1:size(I, dims))./ cumsum(I; dims) .^ 2 .- 1
+
+    (cumsum(I²; dims) .* reshape(1:size(u, dims), sz) ./ cumsum(I; dims) .^ 2 .- 1)
+end
+
+"""
+    cummean(u::AbstractArray{T,N}; dims=N) where {T,N}
+
+Compute the cumulative mean of an array `u` along the specified dimension `dims`. Returns an array of the same size as `u`, containing the cumulative mean along the specified dimension.
+
+"""
+function cummean(u::AbstractArray{T,N}; dims=N) where {T,N}
+    sz = ntuple(i -> i == dims ? size(u, dims) : 1, N)
+    cumsum(u; dims) ./ reshape(1:size(u, dims), sz)
+end
+
+
+"""
+    cumvar(u::AbstractArray{T,N}; dims=N, corrected::Bool=true) where {T,N}
+
+Compute the optionally corrected cumulative variance of an array `u` along the specified dimension `dims`. Returns an array of the same size as `u`, containing the cumulative variance along the specified dimension.
+"""
+function cumvar(u::AbstractArray{T,N}; dims=N, corrected::Bool=true) where {T,N}
+    sz = ntuple(i -> i == dims ? size(u, dims) : 1, N)
+    n = reshape(1:size(u, dims), sz)
+
+    σ² = cummean(u.^2) .- cummean(u).^2
+    if corrected
+        @. σ² *= n / (n - 1)
+    end
+
+    return σ²
 end