  Two classical hypotheses are examined about the population growth in a system
of cities: Hypothesis 1 pertains to Gibrat's and Zipf's theory which states
that the city growth-decay process is size independent; Hypothesis 2 pertains
to the so called Yule process which states that the growth of populations in
cities happens when (i) the distribution of the city population initial size
obeys a log-normal function, (ii) the growth of the settlements follows a
stochastic process. The basis for the test is some official data on Bulgarian
cities at various times. This system was chosen because (i) Bulgaria is a
country for which one does not expect biased theoretical conditions; (ii) the
city populations were determined rather precisely. The present results show
that: (i) the population size growth of the Bulgarian cities is size dependent,
whence Hypothesis 1 is not confirmed for Bulgaria; (ii) the population size
growth of Bulgarian cities can be described by a double Pareto log-normal
distribution, whence Hypothesis 2 is valid for the Bulgarian city system. It is
expected that this fine study brings some information and light on other,
usually considered to be more pertinent, city systems in various countries.
