The famous de Moivre's Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre's Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.

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.

Nigeria is faced with substantial economic and health burdens caused by tobacco smoking. The economic burden of smoking accounts for approximately 1.3 per cent of Nigeria's GDP. In terms of its health impact, 4.9 per cent of all deaths in 2019 were attributed to smokingrelated diseases. The thousands of Nigerians that die annually from tobacco-induced diseases are no longer able to contribute productively to the economy. Tobacco taxation is one very effective mechanism for reducing the burden of smoking. This paper measures and benchmarks the economic gains and the number of lives that could be saved through increased tobacco taxation in Nigeria. Should the government of Nigeria increase the excise tax to 240 Naira per pack (together with an ad valorem tax of 50 per cent of the CIF/ex-works price), our model predicts that, over 30 years, nearly 150,000 premature deaths could be avoided. This is in addition to the more than 150 per cent increase in government revenue that would also result. The model indicates that the larger the increase in the excise tax, the greater would be its fiscal and public health impact.

The Analysis of Variance (ANOVA) test has long been an essential tool for researchers conducting studies on multiple experimental groups with or without one or more control groups. This article encapsulates the fundamentals of ANOVA for an intended benefit of the reader of scientific literature who does not possess expertise in statistics. The emphasis is on conceptually-based perspectives regarding the use and interpretation of ANOVA results, with minimal coverage of the mathematical foundations. Data entry, checking basic parametric assumptions of ANOVA, descriptive statistics of the data by treatment groups, fitting ANOVA model, statistical significance of the test based on p-value, and post-hoc analysis are all explored using R-software.