Add new function

grain_size_tools/GrainSizeTools_script.py

@@ -21,13 +21,6 @@
 #    For details see: http://marcoalopez.github.io/GrainSizeTools/             #
 #    download at https://github.com/marcoalopez/GrainSizeTools/releases        #
 #                                                                              #
-#    Requirements:                                                             #
-#        Python     v3.6 or higher                                             #
-#        Numpy      v1.11 or higher                                            #
-#        Matplotlib v2.0 or higher                                             #
-#        Scipy      v1.0 or higher                                             #
-#        Pandas     v0.16 or higher                                            #
-#                                                                              #
 # ============================================================================ #
 
 # import grain_size_tools modules
@@ -87,6 +80,54 @@ def conf_interval(data, confidence=0.95):
     return amean, err, (low, high)
 
 
+def weighted_mean_and_se(means, standard_errors):
+    """
+    Calculate the weighted mean and standard error of averages
+    using the Mantel-Haenszel method.
+
+    Parameters
+    ----------
+    means : numpy.ndarray
+        1-D array containing the averages.
+    standard_errors : numpy.ndarray
+        1-D array containing the standard errors associated
+        with each average.
+
+    Returns
+    -------
+    float
+        The weighted mean of averages.
+    float
+        The standard error of the weighted mean.
+
+    Raises
+    ------
+    ValueError
+        If input arrays have different shapes.
+
+    Notes
+    -----
+    The function uses the Mantel-Haenszel method to calculate
+    the weighted mean, where each average is weighted by the
+    inverse of its squared standard error. The standard error
+    of the weighted mean is also calculated.
+    """
+    # Ensure the input arrays have the same shape
+    if means.shape != standard_errors.shape:
+        raise ValueError("Input arrays must have the same shape")
+
+    # Calculate the weights based on the inverse of squared standard errors
+    weights = 1 / standard_errors**2
+
+    # Calculate the weighted mean
+    weighted_mean = np.sum(means * weights) / np.sum(weights)
+
+    # Calculate the standard error of the weighted mean
+    se_weighted_mean = 1 / np.sqrt(np.sum(1 / standard_errors**2))
+
+    return weighted_mean, se_weighted_mean
+
+
 def summarize(data, avg=('amean', 'gmean', 'median', 'mode'), ci_level=0.95,
               bandwidth='silverman', precision=0.1):
     """ Estimate different grain size statistics. This includes different means,