  We consider a two-parameter discrete generalized beta (DGB) distribution and
propose its universal applications to study the size-distribution of the urban
agglomerations across various countries in the world, where the urban
agglomerations include the small and mid-sized cities along with the heavily
populated cities. Our proposition is validated by an exhaustive study with the
3 decades' census data for India and China and census data of USA for a time
window of 8 years. Moreover, we have studied the city size distributions for
many different countries, like Brazil, Italy, Sweden, Australia, Uganda etc.,
from all the continents around the world according to the availability of the
data. The detailed analyses exhibit a unique global pattern for the city size
distributions, from low to high size, across the world with various geographic
and economic conditions. Further analyses based on the entropy of the
distribution provide insights on the underlying randomness and spreads of the
city sizes within a country. The DGB distribution, a typical rank order (RO)
distribution, through its two parameters, not only fits the data on wider range
of city sizes better than the well-known power law for all the countries
considered, it also helps us to characterize, discriminate and study their
evolution over time.
