  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 $KS2$.
