*Article* **A Skew Logistic Distribution for Modelling COVID-19 Waves and Its Evaluation Using the Empirical Survival Jensen–Shannon Divergence**

**Mark Levene**

Department of Computer Science and Information Systems, Birkbeck, University of London, London WC1E 7HX, UK; mlevene@dcs.bbk.ac.uk

**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 (E*SJS*) and the Kolmogorov–Smirnov two-sample test statistic (*KS*2). 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 E*SJS* are narrower than those for the *KS*2 on using this dataset, implying that the E*SJS* is more powerful than the *KS*2.

**Keywords:** empirical survival Jensen–Shannon divergence; Kolmogorov–Smirnov two-sample test; skew logistic distribution; bi-logistic growth; epidemic waves; COVID-19 data
