Generalized trapezoidal ogive curves for fatality rate modeling
Abstract
The construction of a continuous family of distributions on a compact set is demonstrated by concatenating, in a continuous manner, three probability density functions with bounded support using a modified mixture technique. The construction technique is similar to that of generalized trapezoidal (GT) distributions, but contrary to GT distributions, the resulting density function is smooth within its bounded domain. The construction of Generalized Trapezoidal Ogive (GTO) distributions was motivated by the COVID19 epidemic, where smoothness of an infection rate curve may be a desirable property combined with the ability to separately model three stages and their durations as the epidemic progresses, being: (1) an increasing infection rate stage, (2) an infection rate stage of some stability and (3) a decreasing infection rate stage. The resulting model allows for asymmetry of the infection rate curve opposite to, for example, the Gaussian Error Infection (GEI) rate curve utilized early on for COVID19 epidemic projections by the Institute for Health Metrics and Evaluation (IHME). While other asymmetric distributions too allow for the modeling of asymmetry, the ability to separately model the above three stages of an epidemic's progression is a distinct feature of the model proposed. The latter avoids unrealistic projections of an epidemic's righttail in the absence of right tail data, which is an artifact of any fatality rate model where a lefttail fit determines its righttail behavior.
 Publication:

Chaos Solitons and Fractals: X
 Pub Date:
 March 2020
 DOI:
 10.1016/j.csfx.2020.100043
 Bibcode:
 2020CSFX....500043D
 Keywords:

 Least squares curve fitting;
 Distribution theory;
 Forecasting