It is quite easy to stochastically distort an original count variable to obtain a new count variable with relatively more variability than in the original variable. Many popular overdispersion models (variance greater than mean) can indeed be obtained by mixtures, compounding or randomlystopped sums. There is no analogous stochastic mechanism for the construction of underdispersed count variables (variance less than mean), starting from an original count distribution of interest. This work proposes a generic method to stochastically distort an original count variable to obtain a new count variable with relatively less variability than in the original variable. The proposed mechanism, termed condensation, attracts probability masses from the quantiles in the tails of the original distribution and redirect them toward quantiles around the expected value. If the original distribution can be simulated, then the simulation of variates from a condensed distribution is straightforward. Moreover, condensed distributions have a simple mean-parametrization, a characteristic useful in a count regression context. An application to the negative binomial distribution resulted in a distribution allowing under, equi and overdispersion. In addition to graphical insights, fields of applications of special cases of condensed Poisson and condensed negative binomial distributions were pointed out as an indication of the potential of condensation for a flexible analysis of count data

This study investigates the process of planning for future inpatient resources (beds, staff and costs) for maternity (pregnancy and childbirth) services. The process of planning is approached from a patient centered philosophy; hence, how do we discharge a suitably rested healthy mother who is fully capable of caring for the newborn baby back into the community. It demonstrates some of the difficulties in predicting future births and investigates trends in the average length of stay. While it is relatively easy to document longer-term (past) trends in births and the conditions relating to pregnancy and birth, it is exceedingly difficult to predict the future nature of such trends. The issue of optimum average bed occupancy is addressed via the Erlang B equation which links number of beds, average bed occupancy and turn-away. Turn-away is the proportion of times that there is not an immediately available bed for the next arriving inpatient. Economy of scale implied by queuing theory (and the implied role of population density) explains why many well intended community-based schemes fail to gain traction. The paper also addresses some of the erroneous ideas around the dogma that reducing length of stay ‘saves’ money. Maternity departments are encouraged to understand how their costs are calculated to avoid the trap where it is suggested by others that in reducing the length of stay, they will reduce costs and increase ‘efficiency’. Indeed, up to 60% of calculated maternity ‘costs’ are apportioned hospital overheads from supporting departments such as finance, personnel, buildings and grounds, IT, information, etc., along with depreciation charges on the hospital-wide buildings and equipment. These costs, “the fixed costs dilemma”, are totally beyond the control of the maternity department and will vary by hospital depending on how these costs are apportioned to the maternity unit. Premature discharge, one of the unfortunate outcomes of turn-away, is demonstrated to shift maternity costs into the pediatric and neonatal departments as ‘boomerang babies’ then require the cost of avoidable inpatient care. Examples are given from the English NHS of how misdirected government policy can create unforeseen problems.