From 5fcc1093db73939983bdd3119be381ed14e1db7b Mon Sep 17 00:00:00 2001
From: "Steven Paul Sanderson II, MPH" <spsanderson@users.noreply.github.com>
Date: Sun, 7 Jan 2024 10:58:33 -0500
Subject: [PATCH] Fixes #374

---
 NEWS.md                      |  2 ++
 R/vec-cumulative-functions.R | 27 ++++++++++++++++++++++++---
 2 files changed, 26 insertions(+), 3 deletions(-)

diff --git a/NEWS.md b/NEWS.md
index ff131933..385b12d0 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -26,6 +26,8 @@ dplyr in favor of using `dplyr::pick()`
 5. Fix #385 - For `tidy_multi_dist_autoplot()` the `.plot_type = "quantile"` did
 not work.
 6. Fix #383 - Update all autoplot functions to use linewidth instead of size.
+7. Fix #375 - Update `cskewness()` to take advantage of vectorization with a speedup
+of 124x faster.
 
 # TidyDensity 1.2.6
 
diff --git a/R/vec-cumulative-functions.R b/R/vec-cumulative-functions.R
index 2c97765c..2ab6575d 100644
--- a/R/vec-cumulative-functions.R
+++ b/R/vec-cumulative-functions.R
@@ -62,10 +62,31 @@ cvar <- function(.x) {
 #'
 
 cskewness <- function(.x) {
-  skewness <- function(.x) {
-    sqrt(length(.x)) * sum((.x - mean(.x))^3) / (sum((.x - mean(.x))^2)^(3 / 2))
+  n <- length(.x)
+
+  if (n == 0L) {
+    return(.x)
+  } else if (n == 1L) {
+    return(0)
+  }
+
+  m2 <- m3  <- term1 <- 0
+  out <- numeric(n)
+  out[1] <- NaN
+  m1 <- .x[1]
+
+  for (i in 2:n) {
+    n0 <- i - 1
+    delta <- x[i] - m1
+    delta_n <- delta/i
+    m1 <- m1 + delta_n
+    term1 <- delta*delta_n*n0
+    m3 <- m3 + term1*delta_n*(n0 - 1) - 3*delta_n*m2
+    m2 <- m2 + term1
+    out[i] <- sqrt(i)*m3/m2^1.5
   }
-  sapply(seq_along(.x), function(k, z) skewness(z[1:k]), z = .x)
+
+  out
 }
 
 #' Cumulative Kurtosis