![]() ![]() When k = 1, the NB distribution reduces to the geometric distribution. The Poisson distribution is obtained as k→∞, and the logarithmic series distribution is obtained as k→0. The distribution is commonly expressed in terms of the mean m and dispersion parameter k such that the probability of observing a non-negative integer x is 1The variance of the NB distribution is m (1+ m/ k), and hence decreasing values of k correspond to increasing levels of dispersion. The popularity of the NB distribution is due largely to its ability to model count data with varying degrees of overdispersion. This study uses simulated data to assess the bias and precision of NB parameter estimates and the coverage accuracy of CIs for highly overdispersed datasets, addressing the challenges of small datasets as well as potential biases arising in the data collection process. A particular concern is whether the results were influenced by small sample size in the datasets analyzed, or biases peculiar to disease transmission data. However, the authors emphasized the challenges inherent in estimating NB parameters and the confidence intervals (CIs) associated with those estimates, and noted that previous work on NB parameter estimation had not explored the parameter ranges of interest for epidemiological studies. Estimation of NB parameters for empirical offspring distributions revealed a high degree of overdispersion-particularly for severe acute respiratory syndrome (SARS), measles, and smallpox-signalling an unexpectedly large influence of individual variation and ‘superspreading’ on the dynamics of disease emergence. The offspring distribution, a concept arising in the theory of branching processes, is the probability distribution for the number of individuals (termed ‘secondary cases’) infected directly by each infectious individual in a disease outbreak. The range of applications of the NB distribution was extended recently to include the epidemiology of directly-transmitted infections, as the NB distribution was shown to be a suitable model for the ‘offspring distribution’ for a number of disease transmission datasets. In the biological literature, classical uses of the NB distribution include analysis of parasite loads, species occurrence, parasitoid attacks, abundance samples and spatial clustering of populations –. with sample variance exceeding the mean). The negative binomial (NB) distribution has broad applications as a model for count data, particularly for data exhibiting overdispersion (i.e. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |