A skew logistic distribution with application to modelling COVID-19 epidemic waves

TL;DR

This paper introduces a skew logistic distribution with a skewness parameter, extends it to model multiple COVID-19 epidemic waves, and validates its effectiveness against other distributions using real data and statistical tests.

Contribution

It proposes a new skew logistic distribution and its extension for epidemic modeling, with a novel validation approach using ${ m ESJS}$ and bootstrap confidence intervals.

Findings

Skew logistic distribution fits COVID-19 data better than symmetric models.

The ${ m ESJS}$ divergence is more sensitive than $KS2$ in goodness-of-fit assessment.

Bootstrap confidence intervals confirm the improved fit of the skew logistic model.

Abstract

A novel yet simple extension of the symmetric logistic distribution is proposed by introducing a skewness parameter. It is shown how the three parameters of the ensuing skew logistic distribution may be estimated using maximum likelihood. The skew logistic distribution is then extended to the skew bi-logistic distribution to allow the modelling of multiple waves in epidemic time series data. The proposed skew-logistic model is validated on COVID-19 data from the UK, and is evaluated for goodness-of-fit against the logistic and normal distributions using the recently formulated empirical survival Jensen-Shannon divergence (${\cal E}SJS$) and the Kolmogorov-Smirnov two-sample test statistic ($KS2$). We employ 95\% bootstrap confidence intervals to assess the improvement in goodness-of-fit of the skew logistic distribution over the other distributions. The obtained confidence intervals for the ${\cal E}SJS$ are narrower than those for the $KS2$ on using this data set, implying that the ${\cal E}SJS$ is more powerful than the $KS2$.