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

by Mark Levene

Entropy 2022, 24(5), 600; https://doi.org/10.3390/e24050600 - 25 Apr 2022

Cited by 5 | Viewed by 3538

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 S J S

) and the Kolmogorov–Smirnov two-sample test statistic (

K S 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 S J S

are narrower than those for the

K S 2

on using this dataset, implying that the

E S J S

is more powerful than the

K S 2

. Full article

(This article belongs to the Special Issue Information and Divergence Measures)

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8 pages, 458 KB

Open AccessProceeding Paper

A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

by Mark Levene

Eng. Proc. 2021, 5(1), 10; https://doi.org/10.3390/engproc2021005010 - 25 Jun 2021

Cited by 4 | Viewed by 2617

Abstract

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (

E S J S

) and the Kolmogorov–Smirnov two-sample test statistic (

K S 2

), are compared [...] Read more.

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (

E S J S

) and the Kolmogorov–Smirnov two-sample test statistic (

K S 2

), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed

α

-stable distributions with

1 < α < 2

at the 95% confidence level. Moreover,

E S J S

is more powerful than

K S 2

on these data sets, since the widths of the derived confidence intervals for

K S 2

are, proportionately, much larger than those of

E S J S

. Full article

(This article belongs to the Proceedings of The 7th International Conference on Time Series and Forecasting)

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