Page 42 - IJPS-8-2

International Journal of
Population Studies Used versus Offered densities of human population

2.1.2. Spatial units as a statistical population Thus x = x , as could be expected.
O
Z
When zones are used to analyze the statistical distribution 2.2.2. On the statistical moments of human density
of some spatial variables in a discrete way, they are often
called “spatial units.” Here, we shall rather refer to zones Higher order moments of human density in the statistical
as “spatial entities” and define “land units” as elementary population of land units are defined in the usual way (e.g.,
places of unit ground area, say a . Such land units are more Blitzstein & Hwang, 2015): At order r,
1
convenientthan zones to constitute the statistical population E []x x r f . (7)
xdx
r
of places since, being identical in area, it is easier to compare O O
them in other respects such as the human population.
Under the idealized assumption that human density
The assignment of land units o to any zone z is an would be homogenous among the land units composing
idealization: Thinking of the unit ground area a as 1 any zone (i.e., no intra-zonal heterogeneity of density),
1
square km or 1 hectare, we expect most zones to involve a then E x E x[], wherein the inter-zone average E
r
r
O
non-integer number of land units. We nevertheless denote Z r Z
as “ o∈z” the composition of zone z out of land units o. of density moment x is defined as
To every land unit o, with population denoted by p , is E []x A z ( P z ) r (8)
r
o
associated a human density as follows: Z A A
z Z Z z
x = p / a 1 (3) r
o
o
O

Notionally, the zone area adds up those of the land units The formula enables one to calculate E x in an
in it, and similarly, the zone population adds up those of exact way under intra-zonal homogeneity of density, or in
an approximate way otherwise.
its land units:
A a (4a) 2.2.3. Indicators of offered human density
z 1 heterogeneity
oz

z
P p o (4b) Local human density is likely to be heterogeneous among
land units, even inside every zone z. The intra-zone variance

oz
of human density is a metric for that heterogeneity within z.
2.2. Human density in the statistical population of It is defined as V x E x 2 |oz E ( | xo z ,
() z
2
)
land units O O O
and satisfies that
Human density x constitutes a random variable in the

statistical population of land units, with PDF and CDF V x a 1 x o x 2 (9)
2
()z
O
denoted by f and F , respectively. A z z
oz
O
O
2.2.1. Average human density over space Over the territory, the overall variance of human
density can be measured using the law of total variance,
The average human density over space stems from the that is, its decomposition into within-group variance and
probability density function f in the usual way (e.g., between-group variance (e.g., Blitzstein & Hwang, 2015):
O
Blitzstein & Hwang, 2015):

O
z ()
O
O
xdx
.
x x f (5) V x A z V x A z ( x x ) 2 (10)
O
z
O
z Z A Z z Z A Z
This general version of average human density over The associated standard deviation (SD) and relative
space is equivalent to the discretized one: Denoting as O dispersion (coefficient of variation, CV) are therefore
the total number of land units, it holds that:
SD x V x (11a)
O
O
x
x o O o x SD x / x (11b)
O
O
O
O
O
As Oa. 1 = A , replacing x with p /a and aO with A In empirical distributions, the variance and, in turn, the
1
Z
o
1
Z
o
due to (4a) aggregated over zone set Z, it comes out that SD and CV are sensitive to outliers, that is, values falling
out of the ordinary range of the variable. As the quantile
P 1
x = A Z Z (6) values F O () at probability level α neither too small nor
O
Volume 8 Issue 2 (2022) 36 https://doi.org/10.36922/ijps.v8i2.297