diff --git a/ReleaseNotes/release_notes.md b/ReleaseNotes/release_notes.md
index 782ce1cb..7542e5a9 100644
--- a/ReleaseNotes/release_notes.md
+++ b/ReleaseNotes/release_notes.md
@@ -12,14 +12,17 @@
1. small fixes for `ostap.utuls.split_ranges`
1. add conversion to int for `RooAbsCategory`
1. add iterator/contains/len functions for `RooAbsDataStore`
-
+ 1. add some simple utilities for goodness-of-fit studies `ostap.stats.gof`
+
## Backward incompatible:
- 1. change the interface for fuctions from `ostap.stats.ustat` module
- 1. change the interface for `Ostap::UStat` class
+ 1. change the interface for functions from the `ostap.stats.ustat` module
+ 1. change the interface for the `Ostap::UStat` class
## Bug fixes:
+ 1. fix a newly introduced bug in `ostap.utils.utils.split_range`
+`
# v1.10.0.2
diff --git a/ostap/stats/gof.py b/ostap/stats/gof.py
new file mode 100644
index 00000000..5990a741
--- /dev/null
+++ b/ostap/stats/gof.py
@@ -0,0 +1,230 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+# =============================================================================
+## @file ostap/stats/gof.py
+# Set of utulities for goodness-of-fit studies
+# @author Vanya BELYAEV Ivan.Belyaev@cern.ch
+# @date 2023-12-06
+# =============================================================================
+""" Simple utulities for goodness-of-fit studies
+"""
+# =============================================================================
+__version__ = "$Revision$"
+__author__ = "Vanya BELYAEV Ivan.Belyaev@cern.ch"
+__date__ = "2023-12-06"
+__all__ = (
+ 'nEff' , ## get number of effective entries
+ 'mean_var' , ## mean and variance for (weighted) arrays
+ 'normalize' , ## "normalize" variables in dataset/structured array
+ )
+# =============================================================================
+from ostap.core.core import VE, Ostap
+from ostap.core.ostap_types import string_types
+# =============================================================================
+try :
+ import numpy as np
+ _np_floats = np.float16, np.float32, np.float64, np.float128
+except ImportError :
+ np = None
+# =============================================================================
+# logging
+# =============================================================================
+from ostap.logger.logger import getLogger
+if '__main__' == __name__ : logger = getLogger( 'ostap.stats.gof' )
+else : logger = getLogger( __name__ )
+# =============================================================================
+logger.debug( 'Simple utilities for goodness-of-fit studies')
+
+
+# ============================================================================
+## Get the mean and variance for (1D) data array with optional (1D) weight array
+# @code
+# ds = ... ## dataste as structured array
+# mean, cov2 = mean_var ( ds ['x'] )
+# @endcode
+# - with weight
+# @code
+# ds = ... ## dataset as structured array with weight
+# mean, cov2 = mean_var ( ds ['x'] , ds['weight'] )
+# @endcode
+def mean_var ( data , weight = None ) :
+ """Get the mean and variance for 1D-data array with optional 1D-weight array
+
+ >>> ds = ... ## dataste as structured array
+ >>> mean, cov2 = mean_var ( ds ['x'] )
+
+ - with weight
+
+ >>> ds = ... ## dataset as structured array with weight
+ >>> mean, cov2 = mean_var ( ds ['x'] , ds['weight'] )
+ """
+ #
+ if weight is None :
+ mean = np.mean ( data , axis = 0 , dtype = np.float64 )
+ var = np.var ( data , axis = 0 , dtype = np.float64 )
+ return mean , var
+ #
+ mean = np.average ( data , weights = weight , axis = 0 )
+ var = np.average ( ( data - mean ) ** 2 , weights = weight , axis = 0 )
+ #
+ return mean , var
+
+# =============================================================================
+## Get the effectibe number of entries for 1D-array
+# \f{ n_{eff} = \frac{ \left\langle x \right\rangle^2}
+# { \left\langle x^2 \right\rangle } \f}
+def nEff ( weights ) :
+ """Get the effectibe number of entries for 1D-array
+
+ n_eff = ( sum ( x ) ) ^2 / sum ( x^2 )
+ """
+
+ s1 = np.sum ( weights , dtype = np.float64 )
+ s2 = np.sum ( weights ** 2 , dtype = np.float64 )
+
+ return s1 * s1 / s2
+
+# =============================================================================
+## Get the "normalized" input datasets
+# All floating felds are calculated as
+# \f[ x = \frac{x - \left\langle x \right\rangle}{\sigma} \f]
+# where \f$ \left\langle x \right\rangle\f$ is mena value
+# and \f$ \sigma \f$ is a standard deviation.
+#
+# @code
+# ds = ... # data set as structured array
+# dsn = normalize ( ds )
+# @endcode
+#
+# - If several datasets are specified, all floating names must be the same
+# and the mean and sigma are either taken either from the first dataset,
+# if first=True or as combined through all datasets otherwise
+#
+# @code
+# ds1 = ... # data set as structured array
+# ds2 = ... # data set as structured array
+# ds3 = ... # data set as structured array
+# ds1n, ds2n, ds3n = normalize ( ds1 , ds2 , ds3 , first = True )
+# @endcode
+#
+# - If weight is specified, this floating column is considered
+# as the weight
+#
+# @code
+# ds = ... # data set as structured array with weight
+# dsn = normalize ( ds , weight = 'weight' )
+# @endcode
+#
+# @code
+# ds1 = ... # data set as structured array without weight
+# ds2 = ... # data set as structured array with weight
+# ds1n , ds2n = normalize ( ds1 , ds2 , weight = ( None , 'weight' ) )
+# @endcode
+#
+# @attention Only the floating point columns are transformed!
+# @attention Input datasets are expected to be numpy structured arrays
+#
+# @code
+# ds = ... # data set as structured array
+# dsn = normalize ( ds )
+# @endcode
+def normalize ( ds , *others , weight = () , first = True ) :
+ """ Get the `normalized' input datasets
+ All floating felds are calculated as
+
+ x = (x - )/sigma
+
+ - is a mean value
+ - is a standard deviation.
+
+ - If several datasets are specified, all floating names must be the same
+ and the mean and sigma are either taken either from the first dataset,
+ if `first=True` or as combined through all datasets, otherwise
+
+ - If `weight` is specified, this floating column is concidered
+ as the weight
+
+ - attention Only the floating point columns are transformed!
+ - attention Input datasets are expected to be numpy structured arrays
+ """
+
+ if not weight :
+ weight = ( len ( others ) + 1 ) * [ '' ]
+ elif isinstance ( weight , string_types ) :
+ weight = [ weight] + len ( others ) * [ '' ]
+
+ assert ( len ( weight ) == len ( others ) + 1 ) and \
+ all ( ( not w ) or isinstance ( w , string_types ) for w in weight ) , \
+ 'Invalid specification of weight!'
+
+ weight = list ( weight )
+ for i,w in enumerate ( weight ) :
+ if not w : weight [ i ] = ''
+ weight = tuple ( weight )
+
+ data = ( ds , ) + others
+ result = []
+
+ ## collect the floating columns
+ columns = []
+ w0 = weight [ 0 ]
+ for n,t in ds.dtype.fields.items () :
+ if t[0] in _np_floats and n != w0 : columns.append ( n )
+
+
+ vmeans = []
+ for i , c in enumerate ( columns ) :
+ mean, var = mean_var ( ds [ c ] , None if not weight [ 0 ] else ds [ weight [ 0] ] )
+ vmeans.append ( VE ( mean , var ) )
+
+ ## Number of events/effective entries
+ nevents = 1.0 * ds.shape [ 0 ] if not weight [ 0 ] else nEff ( ds [ weight [ 0 ] ] )
+
+ if not first and others :
+ nevents = ds.shape[0]
+ for k , dd in others :
+
+ nn = 1.0 * dd.shape [ 0 ] if not weight [ k ] else nEff ( dd [ weight [ k ] ] )
+
+ for i , c in enumerate ( columns ) :
+
+ mean, var = mean_var ( dd [ c ] , None if not weight [ k ] else dd [ weight [ k ] ] )
+
+ vv = VE ( mean , var )
+ nn = dd.shape [ 0 ]
+
+ vmean [ i ] = Ostap.Math.two_samples ( vmean [ i ] , nevents , vv , nn )
+
+ nevents += nn
+
+
+ result = []
+ for k , d in enumerate ( ( ds , *others ) ) :
+ nds = d.copy ()
+ result.append ( nds )
+ for ic,c in enumerate ( columns ) :
+ a = nds [ c ]
+ vv = vmeans [ ic ]
+ mean = vv.value ()
+ sigma = vv.error ()
+
+ nds [ c ] = ( a - mean ) / sigma
+
+
+
+ return result [ 0 ] if not others else tuple ( result )
+
+
+# =============================================================================
+if '__main__' == __name__ :
+
+ from ostap.utils.docme import docme
+ docme ( __name__ , logger = logger )
+
+
+# =============================================================================
+## The END
+# =============================================================================
+
+
+