Added corrected option to many stats methods.

* Reverts many test changes from the last commit
* Changed a bunch of test cases to use `corrected=false` for now
* This included a lot of little changes to method definition and some resulting formatting changes where necessary
* Added a few test cases for the corrected variances
* Added bias correction for ProbabililtyWeights.
* Deprecated `WeightVec`
* Added a macro for easier creation of weight types.
* Renamed weight creation function to `fweights`, `pweights`, etc.

src/StatsBase.jl

@@ -18,11 +18,15 @@ module StatsBase
 
     ## weights
     AbstractWeights,   # the abstract type to represent any weight vector
-    Weights,           # the default type for representing a weight vector
+    AnalyticWeights,   # the default type for representing a analytic/precision/reliability weight vectors
     FrequencyWeights,  # the type for representing a frequency weight vectors
-    weights,     # construct a weights vector
-    frequency,   # construct a frequency weights vector
-    exponential, # construct a weights vector using a exponential smoothing schema
+    ProbabilityWeights,# the type for representing a probability/sampling weight vectors
+    ExponentialWeights,# the type for representing exponential weights
+    weights,           # alias for aweights
+    aweights,          # construct an AnalyticWeights vector
+    fweights,          # construct a FrequencyWeights vector
+    pweights,          # construct a ProbabilityWeights vector
+    eweights,          # construct an ExponentialWeights vector
     wsum,        # weighted sum with vector as second argument
     wsum!,       # weighted sum across dimensions with provided storage
     wmean,       # weighted mean

src/cov.jl

@@ -81,16 +81,17 @@ function mean_and_cov end
     end
 
     ## weighted cov
-    Base.cov(x::DenseMatrix, wv::AbstractWeights; mean=nothing, vardim::Int=1) =
-        scale!(scattermat(x, wv; mean=mean, vardim=vardim), inv(bias(wv)))
+    function Base.cov(x::DenseMatrix, wv::AbstractWeights; mean=nothing, vardim::Int=1, corrected=true)
+        scale!(scattermat(x, wv; mean=mean, vardim=vardim), bias(wv, corrected))
+    end
 
-    function mean_and_cov(x::DenseMatrix; vardim::Int=1)
+    function mean_and_cov(x::DenseMatrix; vardim::Int=1, corrected=true)
         m = mean(x, vardim)
-        return m, Base.covm(x, m; vardim=vardim)
+        return m, Base.covm(x, m; vardim=vardim, corrected=corrected)
     end
-    function mean_and_cov(x::DenseMatrix, wv::AbstractWeights; vardim::Int=1)
+    function mean_and_cov(x::DenseMatrix, wv::AbstractWeights; vardim::Int=1, corrected=true)
         m = mean(x, wv, vardim)
-        return m, Base.cov(x, wv; mean=m, vardim=vardim)
+        return m, Base.cov(x, wv; mean=m, vardim=vardim, corrected=corrected)
     end
 else
     scattermatm(x::DenseMatrix, mean, vardim::Int=1) =
@@ -106,18 +107,21 @@ else
         scattermatm(x, Base.mean(x, wv, vardim), wv, vardim)
 
     ## weighted cov
-    Base.covm(x::DenseMatrix, mean, wv::AbstractWeights, vardim::Int=1) =
-        scale!(scattermatm(x, mean, wv, vardim), inv(bias(wv)))
+    function Base.covm(x::DenseMatrix, mean, wv::AbstractWeights, vardim::Int=1, corrected::Bool=true)
+        scale!(scattermatm(x, mean, wv, vardim), bias(wv, corrected))
+    end
 
-    Base.cov(x::DenseMatrix, wv::AbstractWeights, vardim::Int=1) =
-        Base.covm(x, Base.mean(x, wv, vardim), wv, vardim)
+    function Base.cov(x::DenseMatrix, wv::AbstractWeights, vardim::Int=1; corrected=true)
+        Base.covm(x, Base.mean(x, wv, vardim), wv, vardim, corrected)
+    end
 
-    function mean_and_cov(x::DenseMatrix, vardim::Int=1)
+    function mean_and_cov(x::DenseMatrix, vardim::Int=1; corrected=true)
         m = mean(x, vardim)
-        return m, Base.covm(x, m, vardim)
+        return m, Base.covm(x, m, vardim, corrected)
     end
-    function mean_and_cov(x::DenseMatrix, wv::AbstractWeights, vardim::Int=1)
+
+    function mean_and_cov(x::DenseMatrix, wv::AbstractWeights, vardim::Int=1; corrected=true)
         m = mean(x, wv, vardim)
-        return m, Base.cov(x, wv, vardim)
+        return m, Base.cov(x, wv, vardim; corrected=corrected)
     end
 end

src/deprecates.jl

@@ -43,3 +43,5 @@ findat(a::AbstractArray, b::AbstractArray) = findat!(Array{Int}(size(b)), a, b)
 
 @deprecate df(obj::StatisticalModel) dof(obj)
 @deprecate df_residual(obj::StatisticalModel) dof_residual(obj)
+
+@deprecate WeightVec{S<:Real, V<:RealVector}(vs::V, s::S=sum(vs)) AnalyticWeights(vs, s)