B1102
Title: New models for underdispersed count data based on M/M/1 queues
Authors: Amanda Fernandez-Fontelo - Universitat Autonoma de Barcelona (Spain) [presenting]
Pedro Puig - Universitat Autonoma de Barcelona (Spain)
Abstract: In count data the phenomenon of underdispersion is less common than overdispersion. Accordingly, the researchers have been developed a wide range of statistical models which are able to deal with overdispersion, but few one are able to treat with underdispersion. One of these few models is the COMPoisson distribution which is based on the theory of M/M/1 queues. It was introduced assuming that the service rate could depend on the length of the queue following a power function $\mu_n=\mu n^c$, in which $c$ is a constant indicating the degree to which the service rate is affected by the system state, and describing the (over) underdispersion of the data. Similarly, we propose other models for the service rate, like an exponential function $\mu_n=\mu e^{\beta n}$, obtaining in this case an equilibrium distribution expressed as $p_n=\frac{\rho^n}{e^{\beta n (\frac{n+1}{2})}}p_0$ in which the parameter $\beta$ is also able to model the underdispersion of the data. We also propose a graphical procedure to distinguish in which cases are better our distribution than the COMPoisson. This methodology is applied to several examples, one of them is the number of chromosomal aberrations in irradiated cells, useful in Dosimetry.
