Merge pull request #16 from e10v/dev

Add ratio variance and covariance

pyproject.toml

@@ -92,7 +92,7 @@ testpaths = ["tests"]
 [tool.coverage.run]
 source = ["src/tea_tasting"]
 [tool.coverage.report]
-exclude_lines = ["if TYPE_CHECKING:", "pragma: no cover", "    ..."]
+exclude_lines = ["if TYPE_CHECKING:", "pragma: no cover", "@overload"]
 
 
 [tool.pyright]

src/tea_tasting/aggr.py

@@ -113,6 +113,63 @@ def cov(self: Aggregates, left: str | None, right: str | None) -> float | int:
             return 0
         return self._cov[tea_tasting._utils.sorted_tuple(left, right)]
 
+    def ratio_var(
+        self: Aggregates,
+        numer: str | None,
+        denom: str | None,
+    ) -> float | int:
+        """Sample variance of the ratio of two variables using the Delta method.
+
+        References:
+            [Delta method](https://en.wikipedia.org/wiki/Delta_method).
+            [Taylor expansions for the moments of functions of random variables](https://en.wikipedia.org/wiki/Taylor_expansions_for_the_moments_of_functions_of_random_variables).
+
+        Args:
+            numer: Numerator variable name.
+            denom: Denominator variable name.
+
+        Returns:
+            Sample variance of the ratio of two variables.
+        """
+        denom_mean_sq = self.mean(denom) * self.mean(denom)
+        return (
+            self.var(numer)
+            - 2 * self.cov(numer, denom) * self.mean(numer) / self.mean(denom)
+            + self.var(denom) * self.mean(numer) * self.mean(numer) / denom_mean_sq
+        ) / denom_mean_sq
+
+    def ratio_cov(
+        self: Aggregates,
+        left_numer: str | None,
+        left_denom: str | None,
+        right_numer: str | None,
+        right_denom: str | None,
+    ) -> float | int:
+        """Sample covariance of the ratios of variables using the Delta method.
+
+        References:
+            [Delta method](https://en.wikipedia.org/wiki/Delta_method).
+            [Taylor expansions for the moments of functions of random variables](https://en.wikipedia.org/wiki/Taylor_expansions_for_the_moments_of_functions_of_random_variables).
+
+        Args:
+            left_numer: First numerator variable name.
+            left_denom: First denominator variable name.
+            right_numer: Second numerator variable name.
+            right_denom: Second denominator variable name.
+
+        Returns:
+            Sample covariance of the ratios of variables.
+        """
+        left_ratio_of_means = self.mean(left_numer) / self.mean(left_denom)
+        right_ratio_of_means = self.mean(right_numer) / self.mean(right_denom)
+        return (
+            self.cov(left_numer, right_numer)
+            - self.cov(left_numer, right_denom) * right_ratio_of_means
+            - self.cov(left_denom, right_numer) * left_ratio_of_means
+            + self.cov(left_denom, right_denom)
+                * left_ratio_of_means * right_ratio_of_means
+        ) / self.mean(left_denom) / self.mean(right_denom)
+
     def filter(
         self: Aggregates,
         has_count: bool,

tests/test_aggr.py

@@ -15,9 +15,9 @@
 
 
 COUNT = 100
-MEAN = {"x": 1.0, "y": 2}
-VAR = {"x": 3.0, "y": 4}
-COV = {("x", "y"): 5.0}
+MEAN = {"x": 5.0, "y": 4}
+VAR = {"x": 3.0, "y": 2}
+COV = {("x", "y"): 1.0}
 
 @pytest.fixture
 def aggr() -> tea_tasting.aggr.Aggregates:
@@ -67,6 +67,18 @@ def test_aggregates_none(aggr: tea_tasting.aggr.Aggregates):
     assert aggr.cov(None, "y") == 0
     assert aggr.cov("x", None) == 0
 
+def test_aggregates_ratio_var(aggr: tea_tasting.aggr.Aggregates):
+    assert aggr.ratio_var("x", "y") == pytest.approx(0.2265625)
+
+def test_aggregates_ratio_cov():
+    aggr = tea_tasting.aggr.Aggregates(
+        count=None,
+        mean={"a": 8, "b": 7, "c": 6, "d": 5},
+        var={},
+        cov={("a", "c"): 4, ("a", "d"): 3, ("b", "c"): 2, ("b", "d"): 1},
+    )
+    assert aggr.ratio_cov("a", "b", "c", "d") == pytest.approx(-0.0146938775510204)
+
 def test_aggregates_filter(aggr: tea_tasting.aggr.Aggregates):
     filtered_aggr = aggr.filter(
         has_count=False,