adding hillestimator

README.md

@@ -86,6 +86,9 @@ returnlevels(xs)
 
 # mean excess with previous k values
 meanexcess(xs, k)
+
+# Hill estimator for the tail index using the top k largest values
+hillestimator(xs, k)
 ```
 
 ## References

src/ExtremeStats.jl

@@ -27,6 +27,6 @@ export
 
   # statistics
   returnlevels,
-  meanexcess
-
+  meanexcess,
+  hillestimator
 end

src/stats.jl

@@ -43,3 +43,21 @@ function meanexcess(xs::AbstractVector, ks::AbstractVector{Int})
   ys = sort(xs, rev=true)
   [mean(log.(ys[1:k-1])) - log(ys[k]) for k in ks]
 end
+
+"""
+    hillestimator(data, k)
+
+Return the Hill estimator of the tail index for the data `xs` using the top `k` largest values.
+"""
+function hillestimator(xs::AbstractVector, k::Int)
+    sorted_xs = sort(xs, rev=true)
+
+    if k >= length(sorted_xs)
+        error("k must be smaller than the number of data points")
+    end
+
+    sum_log_ratios = sum(log(sorted_xs[i]) - log(sorted_xs[k+1]) for i in 1:k)
+    hill_estimate = sum_log_ratios / k
+
+    return hill_estimate
+end