# Online Program

##### The R-Symmetric CoGaussian Distribution, its Extensions and Generalizations: Estimation of Modal Incubation Periods of Acute Viral Infections

*Saria Salah Awadalla, University of Illinois at Chicago
Govind S. Mudholkar, University of Rochester

Keywords: Unimodality, Mode, Censoring, Box-Cox transformation, trimmed means

The incubation period, defined as the time interval between exposure and diagnosis, is paramount to understanding the natural history of disease, modeling outbreaks, and controlling infection rates. A review of incubation periods, ranging from acute respiratory viral infections such as influenza to human immunodeficiency virus (HIV), suggests that these intervals have unimodal and positively skewed distributions. The mean and median, which tend to exaggerate incubation periods, are typically reported while the mode is often overlooked mainly because there is a lack of simple, convenient estimators for it. This is an unfortunate setback since the mode represents the most likely outcome, is contained in the highest probability-content neighborhood, and it is robust to extreme observations. In this talk, we present the R-symmetric CoGaussian (CoG) distribution, satisfying the density relation $f(\theta x)=f(\theta/x)$, about the mode $\theta$, as a more appropriate and irresistibly convenient alternative model for the analysis of incubation times. Moreover, we show that the maximum likelihood estimator of $\theta$ has a simple and analytically tractable expression, is an effective estimator of mode, and shares many analogous statistical properties with the mean of a normal variate. Furthermore, we show through simulation studies that extensions such as an analog of the Box-Cox transformation, robustness techniques, and a generalization of CoG, yield far better results than existing mode estimators when applied to a variety of right-skewed distributions. Estimates of the most likely incubation periods of various viral infections will be presented, followed by a discussion of the theoretical and practical implications of data censoring and threshold parameters.