API reference


esda.adbscan.ADBSCAN(eps, min_samples[, ...])

A-DBSCAN, as introduced in [].

Gamma Statistic

esda.Gamma(y, w[, operation, standardize, ...])

Gamma index for spatial autocorrelation

Geary Statistics

esda.Geary(y, w[, transformation, permutations])

Global Geary C Autocorrelation statistic

esda.Geary_Local([connectivity, labels, ...])

Local Geary - Univariate

esda.Geary_Local_MV([connectivity, ...])

Local Geary - Multivariate

Getis-Ord Statistics

esda.G(y, w[, permutations])

Global G Autocorrelation Statistic

esda.G_Local(y, w[, transform, ...])

Generalized Local G Autocorrelation

Join Count Statistics

esda.Join_Counts(y, w[, permutations, ...])

Binary Join Counts

Join Count Local Statistics

esda.Join_Counts_Local([connectivity, ...])

Univariate Local Join Count Statistic

esda.Join_Counts_Local_BV([connectivity, ...])

Univariate Local Join Count Statistic

esda.Join_Counts_Local_MV([connectivity, ...])

Multivariate Local Join Count Statistic

LOSH Statistics

esda.LOSH([connectivity, inference])

Local spatial heteroscedasticity (LOSH)

Modifiable Areal Unit Tests

esda.Smaup(n, k, rho)

S-maup: Statistical Test to Measure the Sensitivity to the Modifiable Areal Unit Problem.

Moran Statistics

esda.Moran(y, w[, transformation, ...])

Moran's I Global Autocorrelation Statistic

esda.Moran_BV(x, y, w[, transformation, ...])

Bivariate Moran's I

esda.Moran_BV_matrix(variables, w[, ...])

Bivariate Moran Matrix

esda.Moran_Local(y, w[, transformation, ...])

Local Moran Statistics.

esda.Moran_Local_BV(x, y, w[, ...])

Bivariate Local Moran Statistics.

esda.Moran_Rate(e, b, w[, adjusted, ...])

Adjusted Moran's I Global Autocorrelation Statistic for Rate Variables [AR99]

esda.Moran_Local_Rate(e, b, w[, adjusted, ...])

Adjusted Local Moran Statistics for Rate Variables [AR99].

Shape Statistics


The boundary amplitude (adapted from Wang & Huang (2012)) is the length of the boundary of the convex hull divided by the length of the boundary of the original shape.


ratio of the area of the convex hull to the area of the shape itself

esda.shape.diameter_ratio(collection[, rotated])

The Flaherty & Crumplin (1992) length-width measure, stated as measure LW_7 in [Alt98].


Deviation of a polygon from an equivalent rectangle

esda.shape.form_factor(collection, height)

Computes volumetric compactness


The Isoareal quotient, defined as the ratio of a polygon's perimeter to the perimeter of the equi-areal circle


The Isoperimetric quotient, defined as the ratio of a polygon's area to the area of the equi-perimeter circle.


The Eig & Seitzinger (1981) shape measure, defined as:


The Reock compactness measure, defined by the ratio of areas between the minimum bounding/containing circle of a shape and the shape itself.


Computes the ratio of the second moment of area (like Li et al (2013)) to the moment of area of a circle with the same area.


Computes the moment of inertia of the polygon.


Computes the Normalized Moment of Inertia from Li et al (2013), recognizing that it is the relationship between the area of a shape squared divided by its second moment of area.


The Flaherty & Crumplin (1992) index, OS_3 in [Alt98].


Ratio of the area of the shape to the area of its minimum bounding rotated rectangle


The Taylor reflexive angle index, measure OS_4 in [Alt98]


Using equation listed on en.wikipedia.org/wiki/Second_moment_of_area#Any_polygon, the second moment of area is the sum of the inertia across the x and y axes:


Schumm’s shape index (Schumm (1956) in MacEachren 1985)


Measures how different is a given shape from an equi-areal square

Silhouette Statistics

esda.boundary_silhouette(data, labels, W[, ...])

Compute the observation-level boundary silhouette score [WKR19].

esda.path_silhouette(data, labels, W[, D, ...])

Compute a path silhouette for all observations [Rou87, WKR19].

esda.silhouettes.nearest_label(data, labels)

Find the nearest label in attribute space.

Spatial Pearson Statistics

esda.Spatial_Pearson([connectivity, ...])

Global Spatial Pearson Statistic

Utility Functions

esda.fdr(pvalues[, alpha])

Calculate the p-value cut-off to control for the false discovery rate (FDR) for multiple testing.