wip(growth): calculate key metrics for growth

1. calculate age in days, weeks, and months
2. calculate body mass index for metric and english unities
3. calculate z-score for a given measurement and box-cox parameters (l,
   m, s)
4. calculate centile score for a given measurement and box-cox
   parameters

lib/growth/calc/z_score.ex

@@ -0,0 +1,47 @@
+defmodule Growth.Calc.ZScore do
+  @moduledoc """
+    measures =
+      [
+        [30, -1.7862, 16.9392, 0.1107],
+        [14, -1.3592, 20.4951, 0.12579],
+        [19, -1.6318, 16.049, 0.10038]
+      ]
+    Enum.map(measures, &apply(Growth.Calc.ZScore, :compute, &1))
+  """
+
+  # TODO: (jpd) add documentation and typespecs
+
+  def compute(y, l, m, s) do
+    y
+    |> raw(l, m, s)
+    |> adjust(y, l, m, s)
+  end
+
+  def raw(y, l, m, s) do
+    (:math.pow(y / m, l) - 1) / (s * l)
+  end
+
+  def adjust(zscore, y, l, m, s) when zscore > 3 do
+    [sd2, sd3, _, _] = cutoffs(l, m, s)
+    sd_delta = sd3 - sd2
+    3 + (y - sd3) / sd_delta
+  end
+
+  def adjust(zscore, y, l, m, s) when zscore < -3 do
+    [_, _, sd2, sd3] = cutoffs(l, m, s)
+    sd_delta = sd2 - sd3
+    -3 + (y - sd3) / sd_delta
+  end
+
+  def adjust(zscore, _, _, _, _) do
+    zscore
+  end
+
+  def cutoffs(l, m, s) do
+    Enum.map([2, 3, -2, -3], &cutoff_for_standard_deviation(&1, l, m, s))
+  end
+
+  def cutoff_for_standard_deviation(sd, l, m, s) do
+    m * :math.pow(1 + l * s * sd, 1 / l)
+  end
+end