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

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 ([Formula: see text]) and the Kolmogorov–Smirnov two-sample test statistic ([Formula: see text]). 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 [Formula: see text] are narrower than those for the [Formula: see text] on using this dataset, implying that the [Formula: see text] is more powerful than the [Formula: see text].