diff --git a/CHANGES.rst b/CHANGES.rst
index 49974f805..deaabd36d 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -22,7 +22,8 @@ Breaking changes
 
 Bug fixes
 ^^^^^^^^^
-* Fixed passing ``missing=0`` to ``xclim.core.calendar.convert_calendar`` (:issue:`1562`, :pull:`1563`).
+* Fixed passing ``missing=0`` to ``xclim.core.calendar.convert_calendar``. (:issue:`1562`, :pull:`1563`).
+* Fix wrong `window` attributes in ``xclim.indices.standardized_precipitation_index``, ``xclim.indices.standardized_precipitation_evapotranspiration_index``. (:issue:`1552`  :pull:`1554`).
 
 Internal changes
 ^^^^^^^^^^^^^^^^
diff --git a/docs/references.bib b/docs/references.bib
index 9b11742f2..1c5f49339 100644
--- a/docs/references.bib
+++ b/docs/references.bib
@@ -2103,3 +2103,18 @@ @article{Lafferty2023
    url = {https://www.nature.com/articles/s41612-023-00486-0},
    year = {2023},
 }
+
+@article{thom_1958,
+  title = {A Note on the Gamma Distribution},
+  author = {Thom, H. C. S.},
+  year = {1958},
+  journal = {Monthly Weather Review},
+  volume = {86},
+  number = {4},
+  pages = {117--122},
+  publisher = {{American Meteorological Society}},
+  issn = {1520-0493, 0027-0644},
+  doi = {10.1175/1520-0493(1958)086<0117:ANOTGD>2.0.CO;2},
+  abstract = {Abstract The general properties of the gamma distribution, which has several applications in meteorology, are discussed. A short review of the general properties of good statistical estimators is given. This is applied to the gamma distribution to show that the maximum likelihood estimators are jointly sufficient. A new, simple approximation of the likelihood solutions is given, and the efficiency of the fitting procedure is computed.},
+  chapter = {Monthly Weather Review},
+}
diff --git a/xclim/indices/_agro.py b/xclim/indices/_agro.py
index f8571f669..96fa9f795 100644
--- a/xclim/indices/_agro.py
+++ b/xclim/indices/_agro.py
@@ -1239,6 +1239,7 @@ def standardized_precipitation_index(
     spi = standardized_index(pr, params)
     spi.attrs = params.attrs
     spi.attrs["freq"] = freq or xarray.infer_freq(spi.time)
+    spi.attrs["window"] = window
     spi.attrs["units"] = ""
     return spi
 
diff --git a/xclim/indices/stats.py b/xclim/indices/stats.py
index 8325ba623..7a91e89bc 100644
--- a/xclim/indices/stats.py
+++ b/xclim/indices/stats.py
@@ -476,7 +476,7 @@ def _fit_start(x, dist: str, **fitkwargs: Any) -> tuple[tuple, dict]:
 
     References
     ----------
-    :cite:cts:`coles_introduction_2001,cohen_parameter_2019`
+    :cite:cts:`coles_introduction_2001,cohen_parameter_2019, thom_1958`
 
     """
     x = np.asarray(x)