OnlineSampleStatistics

UnivariateStatistic(T::Type, K::Int)

Construct an empty UnivariateStatistic with element type T, moment order K, and default weight type Int.

UnivariateStatistic(T::Type, K::Int, I::Type)

Construct an empty UnivariateStatistic with element type T, moment order K, and weight type I.

UnivariateStatistic(K::Int, x)

Construct from one sample x with moment order K and default unit weight.

UnivariateStatistic(K::Int, x, w)

Construct from one sample x with one weight w and moment order K.

UnivariateStatistic(T::Type, K::Int, I::Type, x, w)

Construct from one sample x and one weight w with explicit value type T, moment order K, and weight type I.

UnivariateStatistic(T::Type, K::Int, x)

Construct from one sample x (converted to T) with default weight type Int and unit weight.

UnivariateStatistic(T::Type, K::Int, I::Type, x, w)

Construct from one sample x and one weight w with element type T, moment order K, and weight type I.

UnivariateStatistic(T::Type, K::Int, x::AbstractArray)

Construct from an array of samples converted to T.

UnivariateStatistic(K::Int, x::AbstractArray)

Construct from an array of samples with moment order K, inferring value type from x (integer arrays are promoted to Float64).

UnivariateStatistic(K::Int, x::AbstractArray, w::AbstractArray)

Construct from arrays of samples and weights with moment order K.

UnivariateStatistic(T::Type, K::Int, I::Type, x::AbstractArray, w::AbstractArray)

Construct from arrays of samples and weights.

UnivariateStatistic(K::Int)

Construct an empty UnivariateStatistic of type Float64 and order K.

Inner constructor rawmoments can be given as a vector or a NTuple

copy(A::UnivariateStatistic)

Copy (deepcopy) the UnivariateStatistic A to a new object.

empty!(A::UnivariateStatistic)

Reset the UnivariateStatistic `A` to its initial state.

merge!(A::IndependentStatistic, B::IndependentStatistic)

Merge the statistics from independent statistic B into A, updating A in-place.

This operation combines the sample statistics from B into A by fitting A with the data represented by B. After merging, A will contain aggregated statistics from both sources.

Arguments

• A::IndependentStatistic: The target statistic object to be updated (modified in-place)
• B::IndependentStatistic: The source statistic object to merge into A

Returns

• A::IndependentStatistic: The updated statistic object

merge!(A::UnivariateStatistic, B::UnivariateStatistic)

Merges (inplace) the statistics from B into A in-place.

Example

A = UnivariateStatistic(2, [1.0, 0.5])
B = UnivariateStatistic(2, [2.0, 1.5])
merge!(A, B) 
A ≈ UnivariateStatistic(2, [1.0, 0.5, 2.0, 1.5])

merge(A::IndependentStatistic, B::IndependentStatistic)

Merge two independent statistics by combining their data.

Creates a copy of statistic A and fits it with the data from statistic B, returning a new merged statistic C.

Arguments

• A::IndependentStatistic: The first independent statistic
• B::IndependentStatistic: The second independent statistic to merge into A

Returns

• C::IndependentStatistic: A new statistic that is the result of merging A and B

See Also

• merge!: In-place version of merge

show(io::IO, A::UnivariateStatistic)

Pretty-print a UnivariateStatistic object in a readable format with statistics summary.

Displays:

• Number of observations (n)
• Order (number of moments tracked)
• Mean and variance (if available)
• Skewness and kurtosis (if K ≥ 3 or K ≥ 4)

summary(A::IndependentStatistic)

Return a compact one-line summary of the statistic.

    summary(A::UnivariateStatistic)

Return a compact one-line summary of the statistic.

zero(::UnivariateStatistic{T}) where {T<:UnivariateStatistic} 
zero(::Type{UnivariateStatistic{T,K,I,L}}) where {T,K,I,L}

return an empty UnivariateStatistic of type `T` with `K` moments and weights of type `I`.

UnivariateStatistic(K::Int, x::AbstractArray{T}) where {T<:Number}

Constructs a UnivariateStatistic object storing the first K moments from the vector of samples x.

get_moments(x::AbstractArray{UnivariateStatistic}, k::Int)

Retrieve the k-th moments from an array of UnivariateStatistic objects. Returns an array where each element corresponds to the k-th moment of the respective UnivariateStatistic in x.

get_moments(A::UnivariateStatistic, k) -> Number

Compute the k-th moment of a UnivariateStatistic A.

get_rawmoments(x::AbstractArray{UnivariateStatistic}, k::Int)

Retrieve the k-th raw moments from an array of UnivariateStatistic objects. Returns an array where each element corresponds to the k-th raw moment of the respective UnivariateStatistic in x.

get_rawmoments(x::AbstractArray{<:UnivariateStatistic})

Retrieve the raw moments from an array of UnivariateStatistic objects. Returns an array where each element corresponds to the raw moments of the respective UnivariateStatistic in x.

nonnegative(x)

Check if the input x is nonnegative (greater than or equal to zero).

" order(A::UnivariateStatistic) Return the number of moments in a A.

mean(A::UnivariateStatistic)

Compute the sample mean of a A

 std(A::UnivariateStatistic; corrected=true)

Compute the sample standard deviation of a A, from its variance (corrected by default).

 std(A::IndependentStatistic; corrected=true)

Compute the sample standard deviation of a A, from its variance (corrected by default).

var(A::UnivariateStatistic; corrected=true)

Compute the sample variance of a A. If corrected is true, the variance is corrected for bias. The unbias variance estimator is only available for an integer number of sample.

fit!(A::IndependentStatistic{T,N,K}, B::IndependentStatistic)

Merge the accumulated statistics in B into A in-place. A must have compatible element type and size, and its number of moments K must be less than or equal to the one of B.

fit!(A::UnivariateStatistic{T}, y::T2) where {T, T2}

Pushes a new samples y into the UnivariateStatistic A.

Throws

• ArgumentError: If the type of elements in y is not compatible with the type T of A.

nobs(A::UnivariateStatistic)

Return the number of samples or the sum of weights in a A.

weights(x::AbstractArray{UnivariateStatistic})

Retrieves the weights from an array of UnivariateStatistic objects.

weights(A::UnivariateStatistic)

Return the sum of weights in a A.

read(IndependentStatistic, fitsfile::FitsFile, stat_group_id::String; readkwds...)

Read an IndependentStatistic identified by stat_group_id from fitsfile. Extra keyword arguments are forwarded to AstroFITS when reading the weights HDU.

read(IndependentStatistic, fitsfile::FitsFile; ext=1, readkwds...)

Read an IndependentStatistic from fitsfile by taking the group ID from HDU ext. Throws ArgumentError if ext is not a stat HDU or misses STAT-GROUP-ID.

write(file::FitsFile, hdr::AstroFITS.OptionalHeader,
      stat::IndependentStatistic, stat_group_id::String)

Write stat to file using stat_group_id. Throws ArgumentError if stat_group_id is already used by another statistic in the same FITS file.

write(file::FitsFile, hdr::AstroFITS.OptionalHeader, stat::IndependentStatistic)

Write stat to file using a freshly generated unique group ID.

find_stat_group_ids(fitsfile::FitsFile)

Return unique statistic group IDs found in fitsfile. Only HDUs recognized by isa_stat_hdu and carrying the STAT-GROUP-ID keyword are considered.

find_stat_hdus(fitsfile::FitsFile, stat_group_id::String)

Find all HDUs belonging to stat_group_id and return (moments_hdus, weights_hdu, T, N, K, W). Throws ArgumentError if required HDUs or metadata are missing/inconsistent.

isa_stat_hdu(hdu)

Return true if hdu is an image HDU tagged as an OnlineSampleStatistics HDU.

_generate_unique_stat_group_id(file::FitsFile)

Generate a random group ID that is not already present in file.