Modeling COVID-19 Pandemic Data with Beta-Double Exponential Model

Abstract

Objective: This paper examines and upgrades a two-parameter double exponential distribution to a four-parameter beta double exponential model by compounding the baseline distribution and beta link function to fits and analyse deaths-cases data set of the recent outbreak of the global pandemic coronavirus disease (COVID-19) for both Africa and Non-Africa countries. The new proposed model, although complex in its mathematical structure, yet flexible to implement and its robustness to accommodate non-normal data is an extra advantage to statistical theory and other fields.
 Methodology: The statistical properties: the density function, cumulative distribution function, survival function, hazard function, moments, moments generating function, skewness and kurtosis of the developed model were presented. Maximum likelihood method is used for parameters estimation procedure. The new model is validated and compared with some frontier similar extant parametric family of beta distributions using graphs, Kolmogorov Smirnov (KS) Statistic, Log-likelihood and model criteria statistics like Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC) and Consistent Akaike Information Criteria (CAIC) as tools for comparison.
 Results: The graphs, KS, LogL and model criteria statistics values showed that the proposed model fits the COVID-19 pandemic data better than other competing models since the model has lower values as stated: The values from non-African countries KS = 0.1208, LogL = 278.4168, AIC = 560.8336, BIC = 576.1147 and CAIC = 577.1147. Also, from African countries are: KS = 0.0759, LogL = 144.0245, AIC = 292.0490, BIC = 303.9302 and CAIC = 304.9302.
 Conclusion: The proposed model showed its applicability and flexibility over other models considered in this work. Therefore, this implies that the new model can be used for modeling other infectious disease data and real data in many fields.

Parametric Modeling Approach to Covid-19 Pandemic Data

“…Many researches/works have been done by several researchers since the breakup of the pandemic in December 2019 from various fields, such as Medicine, Statistics, Economics, etc., with different ideas, models, methods and approaches in their respective works. These include Badmus et al (2020), Dey et al (2020), WHO, (2020), Yoo, (2020) amongst others [1] [2] [3] [4]. Moharraza et al [5] in their work developed a simple model to assess the spread of global Covid-19 pandemic and tested the validity of their model using the cases of the coronavirus disease compiled by the WHO.…”

“…The main goal of the extensions of the proposed model is to enhance the robustness and flexibility of the classical model. Also, motivating factors, including the model, are a family of beta generalized models in such that when equating one or more parameter(s) to one (1), the model becomes the baseline distribution. In addition, the model has capability to increase and decrease shapes due to heavily skewed and heavy tail probability distribution that plays an important role in modeling skewed data like clinical data.…”