Following the emergence of COVID-19 outbreak, numbers of studies have been conducted to curtail the global spread of the virus by identifying epidemiological changes of the disease through developing statistical models, estimation of the basic reproduction number, displaying the daily reports of confirmed and deaths cases, which are closely related to the present study. Reliable and comprehensive estimation method of the epidemiological data is required to understand the actual situation of fatalities caused by the epidemic. Case fatality rate (CFR) is one of the cardinal epidemiological parameters that adequately explains epidemiology of the outbreak of a disease. In the present study, we employed two statistical regression models such as the linear and polynomial models in order to estimate the CFR, based on the early phase of COVID-19 outbreak in Nigeria (44 days since first reported COVID-19 death). The estimate of the CFR was determined based on cumulative number of confirmed cases and deaths reported from 23 March to 30 April, 2020. The results from the linear model estimated that the CFR was 3.11% (95% CI: 2.59 – 3.80%) with R 2 value of 90% and p -value of < 0.0001. The findings from the polynomial model suggest that the CFR associated with the Nigerian outbreak is 3.0% and may range from 2.23 to 3.42% with R 2 value of 93% and p -value of <0.0001. Therefore, the polynomial regression model with the higher R 2 value fits the dataset well and provides better estimate of CFR for the reported COVID-19 cases in Nigeria.

Groundwater is one of the significant sources of drinking water in the world. To protect groundwater quality for domestic consumption, it is important to undertake a periodic investigation of its quality to improve the healthy living of the ever-increasing population. In this paper, we have analyzed physical and chemical (physicochemical) concentration levels in groundwater samples collected from twenty-eight sampling locations during the raining season in Gwale, Northwest Nigeria. About fifteen physicochemical parameters such as electric conductivity (EC), turbidity (Turb), pH,  temperature (Temp), nitrate (NO3), phosphate (PO4), total dissolved solid (TDS), chloride (Cl), sulphate (SO4), calcium (Ca), magnesium (mg), sodium (Na), total hardness (TH), iron (Fe) and alkalinity (Alk) were analyzed. The concentrations levels of groundwater parameters in each sampling location were compared with the permissible limits of drinking water qualities specified by the Nigerian Industrial Standard (NIS) to determine the suitability of drinking water in the study area. Karl Pearson’s coefficient of correlation was applied to the groundwater dataset to identify the influence of each physicochemical parameter to the groundwater contamination. Also, hierarchical cluster analysis was used to classify the groundwater samples based on contamination density as well as to identify the sources of water contamination. The results from correlation analysis revealed that EC, TDS, Ca, TH, Mg, SO4, Na and Cl were influenced the water contamination in many of the study locations based on the conventional significance levels (1% and 5%). From the results of cluster analysis, three statistically significant groups (cluster 1, cluster 2 and cluster 3) were formed which were defined as lower contaminated areas, moderately contaminated areas and higher contaminated areas, respectively. The contamination levels identified in the three clusters were attributed to anthropogenic and industrial activities in the raining season. Therefore, groundwater from cluster 3 (Salanta, Hauren makaranta, Dandago, Mandawari and Magashi) are found unsuitable for drinking. This study is useful in monitoring groundwater quality and could be applied in any other location.

Multivariate statistical methods, Cluster Analysis (CA) and Canonical Discriminant Analysis (CDA) were applied to assess the temporal and spatial variations, and identify pollution sources in some rivers/streams of Niger State in Nigeria. Sixteen towns were sampled as medium-sized towns in which data were gathered on four physical, eleven chemical and two microbial parameters of water. Hierarchical CA grouped the sixteen sampled sites into four main seasonal clusters and three main groups of similar water quality. Stepwise selection for the temporal Discriminant Analysis (DA) identified the most significant parameters for discriminating between the four seasons as magnesium, Escherichia coli, total coliform, total dissolved solid (TDS) and total hardness with 83.3% apparent correct classification. The stepwise selection for the spatial Discriminant Analysis (DA) show that, Escherichia coli and magnesium is more prevalent in winter; while Escherichia coli and total dissolved solid (TDS) is higher in spring; and Escherichia coli and total coliform were more in summer and autumn with 94% total success rate of classification. The outcome of this study also show that the sources of water in groups one and two were more polluted than group three during summer and autumn than in the winter and spring. Based on these findings, it is recommended that the frequency of monitoring sites could be reduced to only sites in groups one and two while the seasons could be based on summer and autumn.

Two parameters Maxwell – Exponential distribution was proposed using the Maxwell generalized family of distribution. The probability density function, cumulative distribution function, survival function, hazard function, quantile function, and statistical properties of the proposed distribution are discussed. The parameters of the proposed distribution have been estimated using the maximum likelihood estimation method. The potentiality of the estimators was shown using a simulation study. The overall assessment of the performance of Maxwell - Exponential distribution was determined by using two real-life datasets. Our findings reveal that the Maxwell – Exponential distribution is more flexible compared to other competing distributions as it has the least value of information criteria.

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