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CPS1407 D.Dilshanie Deepawansa et al.
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∑ =1 × () ln
=; where = 1 . (4)

∑ =1 ∑ ln
=1

In equation (4), the term denotes the number of individuals who are
completely deprived in the j indicator. The natural logarithm of the inverse
th
of frequency is applied in order that a low value of is not assigned a greater
weight.
There are several methods that can be used to test the robustness of
ranking. The commonly used methods are Spearman rank correlation
coefficient () and Kendall rank correlation coefficient (). In this study, we use
Kendall rank correlation to identify the poverty cut-off (z) because a small
number of subgroups are considered for ranking and Kendall rank correlation
coefficient has lower Gross Error Sensitivity (GES) and smaller asymptotic
variance, making Kendall correlation measure more robust and slightly more
efficient than the Spearman rank correlation (Croux & Dehon, 2010).
Accordingly, we calculate Kendall rank correlation (tau-b) coefficients for
different cut-off points for sub groups of the population we study. is used
In this study, we produce five poverty indices based on the deprivation
scores of individuals as follows:
a) Fuzzy Headcount Index (FHI); b) Fuzzy Intensity (FI);c) Adjusted Fuzzy
Deprivation Index (FM0); d) Normalized Deprivation Gap Index (FM1); and,
e) Squared Normalized Deprivation Gap Index (FM2).
The Fuzzy Headcount Index (FHI) is the percentage of deprived and
multidimensionally poor people. Average Fuzzy Membership Deprivation is
the propensity to be poor. Fuzzy Intensity (FI) is average weighted deprivation
experienced by multidimensionally poor people called intensity of fuzzy
poverty. Adjusted Headcount Index (FM0) is the percentage of deprivation
which poor people experience as a share of possible deprivation that would
be experienced if all the people were deprived in all the dimensions. This is
the key indicator measuring multidimensional deprivation of poverty. The
normalized Deprivation Gap Index (DGI) is sum of aggregated deprivation
difference to poverty cutoff of multidimensional people and divided it by the
deprivation cut-off. It is the depth of deprivation and Squared Deprivation Gap
Index (SDGI) that gives the severity of deprivation. Appendix 1 sets out in detail
how these indices were calculated.

2.2 Data
The analysis uses primary data from the household survey conducted for
the purpose of the study from November 2016 to January 2017 January in the
Uva province of Sri Lanka. According to official statistics on consumption
poverty, Uva has been an economically backward province throughout in the

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