A Poisson regression approach for assessing morbidity risk and determinants among under five children in Nigeria.

In this paper, we have provided more insights on the relationship between under five morbidity in Nigeria and some background characteristics using a Poisson regression model and the most recent 2018 NDHS data on Acute Respiratory Infection (ARI), diarrhoea and fever. Some of our results are that children 36-47 months old have the highest risk of ARI [OR = 1.45; CI (1.31,1.60)] while children less than 6 months old have the lowest risk of ARI [OR = 0.14; CI (0.11,0.17)]. The prevalence of diarrhoea is generally high among children under 48-59 months old but highest among children 6-11 months old [OR = 4.34; CI (3.69,5.09)]. Compared to children 48-59 months old, children in all other age categories except 24-34 months old have a high risk of fever [OR = 0.95; CI (0.73,1.24)]. ARI is more prevalent among female children [OR = 8.88; CI (8.02,9.82)] while diarrhoea [OR = 21.75; (19.10,24.76)] and fever [OR = 4.78; CI (4.31,5.32)] are more prevalent among male children. Children in urban areas are more likely to suffer ARI [OR = 9.49; CI (8.31,10.85)] while children in rural areas are more likely to suffer both diarrhoea [OR = 21.75; CI (19.10,24.76)] and fever [OR = 4.90; CI (4.26,5.63)]. Children in the South-South have the highest risk of ARI [OR = 4.03; CI (3.65,4.454)] while children in the North Central have the lowest risk of ARI [OR = 1.55; CI (1.38,1.74)] and highest risk of diarrhoea [OR = 3.34; CI (2.30,5.11)]. Children in the Northeast have the highest risk of fever [OR = 1.30; CI (1.14,1.48)]. In the Northcentral region, Kogi state has the highest prevalence of fever [OR = 2.27; CI (1.62,3.17)], while Benue state has the lowest [OR = 0.35; CI (0.20,0.60)]. Children in Abuja state face similar risks of fever and diarrhoea [OR = 0.84; CI (0.55,1.27)], with the risk of diarrhoea in Abuja being comparable to that in Plateau state [OR = 1.57; CI (0.92,2.70)]. Nasarawa state records the highest incidence of diarrhoea in the Northcentral [OR = 5.12; CI (3.03,8.65)], whereas Kogi state reports the lowest [OR = 0.29; CI (0.16,0.53)]. In the Northeast, Borno state has the highest rate of fever [OR = 3.28; CI (2.80,3.84)], and Bauchi state the lowest [OR = 0.38; CI (0.29,0.50)]. In Adamawa state, the risks of fever and diarrhoea are nearly equivalent [OR = 1.17; CI (0.97,1.41)], and the risk of fever there is similar to that in Taraba state [OR = 0.92; CI (0.75,1.12)]. Diarrhoea is most prevalent in Yobe state [OR = 3.17; CI (2.37,4.23)] and least prevalent in Borno state [OR = 0.26; CI (0.20,0.33)]. In the Northwest, the risk of fever is similarly high in Zamfara and Kebbi states [OR = 1.04; CI (0.93,1.17)], with Kastina state showing the lowest risk [OR = 0.39; CI (0.34,0.46)]. Children in Zamfara state experience notably different risks of fever and diarrhoea [OR = 0.07; CI (0.05,0.10)]. Kaduna state reports the highest incidence of diarrhoea [OR = 21.88; CI (15.54,30.82)], while Kano state has the lowest [OR = 2.50; CI (1.73,3.63)]. In the Southeast, Imo state leads in fever incidence [OR = 8.20; CI (5.61,11.98)], while Anambra state has the lowest [OR = 0.40; CI (0.21,0.78)]. In Abia state, the risk of fever is comparable to that in Enugu state [OR = 1.03; CI (0.63,1.71)], but the risks of fever and diarrhoea in Abia differ significantly [OR = 2.67; CI (1.75,4.06)]. Abia state also has the highest diarrhoea rate in the Southeast [OR = 2.67; CI (1.75,4.06)], with Ebonyi state having the lowest [OR = 0.05; CI (0.03,0.09)]. In the South-South region, Bayelsa and Edo states have similar risks of fever [OR = 1.28; CI (0.84,1.95)], with Akwa Ibom state reporting the highest fever rate [OR = 4.62; CI (3.27,6.52)] and Delta state the lowest [OR = 0.08; CI (0.02,0.25)]. Children in Bayelsa state face distinctly different risks of fever and diarrhoea [OR = 0.56; CI (0.34,0.95)]. Rivers state shows the highest incidence of diarrhoea in the South-South [OR = 10.50; CI (4.78,23.06)], while Akwa Ibom state has the lowest [OR = 0.30; CI (0.15,0.57)]. In the Southwest, Lagos and Osun states have similar risks of fever [OR = 1.00; CI (0.59,1.69)], with Ogun state experiencing the highest incidence [OR = 3.47; CI (2.28,5.28)] and Oyo state the lowest [OR = 0.18; CI (0.07,0.46)]. In Lagos state, the risks of fever and diarrhoea are comparable [OR = 0.96; CI (0.57,1.64)], and the risk of diarrhoea is similar to those in Ekiti, Ogun, and Ondo states. Oyo state has the highest diarrhoea rate in the Southwest [OR = 10.99; CI (3.81,31.67)], with Ogun state reporting the lowest [OR = 0.77; CI (0.42,1.42)]. Children of mothers with more than secondary education are significantly less likely to suffer ARI [OR = 0.35; CI (0.29,0.42)], whereas children of mothers without any education run a higher risk of diarrhoea [OR = 2.12; CI (1.89,2.38)] and fever [OR = 2.61; CI (2.34,2.91)]. Our analysis also indicated that household wealth quintile is a significant determinant of morbidity. The results in this paper could help the government and non-governmental agencies to focus and target intervention programs for ARI, diarrhoea and fever on the most vulnerable and risky under five groups and populations in Nigeria.

Exact Expressions for Kullback-Leibler Divergence for Multivariate and Matrix-Variate Distributions.

The Kullback-Leibler divergence is a measure of the divergence between two probability distributions, often used in statistics and information theory. However, exact expressions for it are not known for multivariate or matrix-variate distributions apart from a few cases. In this paper, exact expressions for the Kullback-Leibler divergence are derived for over twenty multivariate and matrix-variate distributions. The expressions involve various special functions.

An extreme value analysis of water levels at the Akosombo dam, Ghana.

The Akosombo Dam is the largest dam in Ghana and is linked to the world's largest man-made lake by surface area. The top of flood control pool of the dam has been breached a number of times, so it is of interest to know the corresponding probability. The paper fits the generalized extreme value distribution to the extreme water levels - with all three of its parameters (including the shape parameter) accounting for various linear trends, seasonality and cyclic trends with respect to time, the first time such a model has been fitted. The fitted model contains in total 50 parameters. It provided an adequate fit, as evaluated by probability plots, quantile plots, and the Kolmogorov-Smirnov test. It is used to provide return level estimates as well as probabilities of the top of flood control pool of the dam being breached.

Statistical modeling of maximum temperature in Guinea.

A statistical analysis of maximum temperature from twelve weather stations in parts of Guinea is provided. Using maximum likelihood estimation, maximum temperature data was fitted by the Generalized Extreme Value distribution. Data from all of the twelve stations were adequately fit by the Generalized Extreme Value distribution. Return level estimates are provided. Significant trends in maximum temperature were found for four of the stations. The four stations exhibited significant positive trends at the 5% significance level.

Modeling opening price spread of Shanghai Composite Index based on ARIMA-GRU/LSTM hybrid model.

In the dynamic landscape of financial markets, accurate forecasting of stock indices remains a pivotal yet challenging task, essential for investors and policymakers alike. This study is motivated by the need to enhance the precision of predicting the Shanghai Composite Index's opening price spread, a critical measure reflecting market volatility and investor sentiment. Traditional time series models like ARIMA have shown limitations in capturing the complex, nonlinear patterns inherent in stock price movements, prompting the exploration of advanced methodologies. The aim of this research is to bridge the gap in forecasting accuracy by developing a hybrid model that integrates the strengths of ARIMA with deep learning techniques, specifically Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) networks. This novel approach leverages the ARIMA model's proficiency in linear trend analysis and the deep learning models' capability in modeling nonlinear dependencies, aiming to provide a comprehensive tool for market prediction. Utilizing a comprehensive dataset covering the period from December 20, 1990, to June 2, 2023, the study develops and assesses the efficacy of ARIMA, LSTM, GRU, ARIMA-LSTM, and ARIMA-GRU models in forecasting the Shanghai Composite Index's opening price spread. The evaluation of these models is based on key statistical metrics, including Mean Squared Error (MSE) and Mean Absolute Error (MAE), to gauge their predictive accuracy. The findings indicate that the hybrid models, ARIMA-LSTM and ARIMA-GRU, perform better in forecasting the opening price spread of the Shanghai Composite Index than their standalone counterparts. This outcome suggests that combining traditional statistical methods with advanced deep learning algorithms can enhance stock market prediction. The research contributes to the field by providing evidence of the potential benefits of integrating different modeling approaches for financial forecasting, offering insights that could inform investment strategies and financial decision-making.

Bayesian modeling of maternal mortality in Ghana.

Maternal mortality is a critical measure for quality of health system in any country and hence many countries have made concerted efforts to check its occurrence. Various stakeholders involved in the management of health system in Ghana have been tasked to ensure women do not die whilst giving birth. This study was conducted on a sample of 1,052 women selected from all the ten administrative regions of Ghana in which 188 maternal deaths occurred. Bayesian logistic modeling was used. Age at death, marital status, age, season, region, place of death, place of residence, religion and ethnicity emerged as the most significant determinants of maternal mortality in Ghana. It was realized that high numbers of maternal deaths were recorded in the least developed regions in the northern region. It is therefore important for stakeholders to devise a road map of getting health workers to accept postings to the rural areas and also provide well resourced health facilities to stem this menace.

Integer time series models for tuberculosis in Africa.

Tuberculosis, an airborne disease, is the deadliest human infectious disease caused by one single agent. The African region is among the most affected and most burdensome area in terms of tuberculosis cases. In this paper, we modeled the number of new cases of tuberculosis for 2000-2021 by integer time series. For each African country, we fitted twenty different models and selected the model that best fitted the data. The twenty models were mostly based on the number of new cases following either the Poisson or negative binomial distribution with the rate parameter allowed to vary linearly or quadratically with respect to year. The best fitted models were used to give predictions for 2022-2031.

An extreme value analysis of daily new cases of COVID-19 for sixteen countries in west Africa.

We provide an extreme value analysis of daily new cases of COVID-19. We use data from Benin, Burkina Faso, Cabo Verde, Cote d'Ivoire, Gambia, Ghana, Guinea, Guinea-Bissau, Liberia, Mali, Mauritania, Niger, Nigeria, Senegal, Sierra Leone and Togo, covering a period of 37 months. Extreme values were defined as monthly maximums of daily new cases. The generalized extreme value distribution was fitted to them with two of its three parameters allowed to vary linearly or quadratically with respect to month number. Ten of the sixteen countries were found to exhibit significant downward trends in monthly maximums. The adequacy of fits was assessed by probability plots and the Kolmogorov-Smirnov test. The fitted models were used to derive quantiles of the monthly maximum of new cases as well as their limits when the month number is taken to infinity.

Time series and power law analysis of crop yield in some east African countries.

We carry out a time series analysis on the yearly crop yield data in six east African countries (Burundi, Kenya, Somalia, Tanzania, Uganda and Rwanda) using the autoregressive integrated moving average (ARIMA) model. We describe the upper tail of the yearly crop yield data in those countries using the power law, lognormal, Fréchet and stretched exponential distributions. The forecast of the fitted ARIMA models suggests that the majority of the crops in different countries will experience neither an increase nor a decrease in yield from 2019 to 2028. A few exceptional cases correspond to significant increase in the yield of sorghum and coffee in Burundi and Rwanda, respectively, and significant decrease in the yield of beans in Burundi, Kenya and Rwanda. Based on Vuong's similarity test p-value, we find that the power law distribution captured the upper tails of yield distribution better than other distributions with just one exceptional case in Uganda, suggesting that these crops have the tendency for producing high yield. We find that only sugar cane in Somalia and sweet potato in Tanzania have the potential of producing extremely high yield. We describe the yield behaviour of these two crops as black swan, where the "rich getting richer" or the "preferential attachment" could be the underlying generating process. Other crops in Burundi, Kenya, Somalia, Tanzania, Uganda and Rwanda can only produce high but not extremely high yields. Various climate adaptation/smart strategies (use of short-duration pigeon pea varieties, use of cassava mosaic disease resistant cassava varieties, use of improved maize varieties, intensive manuring with a combination of green and poultry manure, early planting, etc) that could be adapted to increase yields in east Africa are suggested. The paper could be useful for future agricultural planning and rates calibration in crop risk insurance.

New discrete heavy tailed distributions as models for insurance data.

Although many data sets are discrete and heavy tailed (for example, number of claims and claim amounts if recorded as rounded values), not many discrete heavy tailed distributions are available in the literature. In this paper, we discuss thirteen known discrete heavy tailed distributions, propose nine new discrete heavy tailed distributions and give expressions for their probability mass functions, cumulative distribution functions, hazard rate functions, reversed hazard rate functions, means, variances, moment generating functions, entropies and quantile functions. Tail behaviour and a measure of asymmetry are used to compare the known and new discrete heavy tailed distributions. The better fits of the discrete heavy tailed distributions over their continuous counterparts as assessed by probability plots are illustrated using three data sets. Finally, a simulated study is performed to assess the finite sample performance of the maximum likelihood estimators used in the data application section.

Mixture modeling of hospital charge in Zimbabwe.

Objective: Zimbabwe is one of the poorest countries in the world, just emerging from a broken health care system. The objective is to figure out variables affecting hospital charge for Zimbabwe. Material and methods: The variables used are sex, smoking status, number of children, region, age and body mass index. The first six of these are factors and the remaining are covariates. A mixture model was fitted to describe the dependence of hospital charge on these variables. Results: A mixture model with five components each having a reversed Gumbel distribution was found to give an adequate fit. Both the covariates and all but one of the factors were found to be significant. Estimates of value at risk of hospital charge are given for all combinations of the factors. Conclusions: The results suggest that the hospital charge could be higher for females, higher for smokers, higher if the patient had more children and higher if the patient is older. Further, estimates of value at risk given suggest, for example, that a 90 year old female not smoking and having no children and an average body mass index will have a hospital charge less than Z$49851 with probability 0.999.

Explicit Expressions for Most Common Entropies.

Entropies are useful measures of variation. However, explicit expressions for entropies available in the literature are limited. In this paper, we provide a comprehensive collection of explicit expressions for four of the most common entropies for over sixty continuous univariate distributions. Most of the derived expressions are new. The explicit expressions involve known special functions.

Parametric inference of the process capability index for exponentiated exponential distribution.

Process capability indices (PCIs) are most effective devices/techniques used in industries for determining the quality of products and performance of manufacturing processes. In this article, we consider the PCI Cpc which is based on the proportion of conformance and is applicable to normally as well as non-normally and continuous as well as discrete distributed processes. In order to estimate the PCI Cpc when the process follows exponentiated exponential distribution, we have used five classical methods of estimation. The performances of these classical estimators are compared with respect to their biases and mean squared errors (MSEs) of the index Cpc through simulation study. Also, the confidence intervals for the index Cpc are constructed using five bootstrap confidence interval (BCIs) methods. Monte Carlo simulation study has been carried out to compare the performances of these five BCIs in terms of their average width and coverage probabilities. Besides, net sensitivity (NS) analysis for the given PCI Cpc is considered. We use two data sets related to electronic and food industries and two failure time data sets to illustrate the performance of the proposed methods of estimation and BCIs. Additionally, we have developed PCI Cpc using aforementioned methods for generalized Rayleigh distribution.

Forecasting Value at Risk and Expected Shortfall of Foreign Exchange Rate Volatility of Major African Currencies via GARCH and Dynamic Conditional Correlation Analysis.

Research on the exchange rate volatility and dynamic conditional correlation of African currencies/financial markets interdependence appears to be limited. In this paper, we employ GARCH models to characterize the exchange rate volatility of eight major African currencies. The variation of interdependence with respect to time is described using the DCC-GARCH model. From the results of the DCC, remarkable variations in correlations through time across these countries are observed with the correlations varying from low to moderate, suggesting that African economies are generally governed by certain economic factors and are vastly regulated. These regulations, including exchange rate misalignment led to sluggish and negative growth in most of the African countries. For instance, persistent misalignment can cause high levels of inflation, for example, undervaluation. Overvaluation can lead to trade imbalances and they can in turn create macroeconomic instability and balance of payment problems. Given these results, we suggest that policy makers should revamp and adopt state resilience so as to reduce the negative effect of exchange rate misalignment on economic growth.

An Overview of Discrete Distributions in Modelling COVID-19 Data Sets.

The mathematical modeling of the coronavirus disease-19 (COVID-19) pandemic has been attempted by a large number of researchers from the very beginning of cases worldwide. The purpose of this research work is to find and classify the modelling of COVID-19 data by determining the optimal statistical modelling to evaluate the regular count of new COVID-19 fatalities, thus requiring discrete distributions. Some discrete models are checked and reviewed, such as Binomial, Poisson, Hypergeometric, discrete negative binomial, beta-binomial, Skellam, beta negative binomial, Burr, discrete Lindley, discrete alpha power inverse Lomax, discrete generalized exponential, discrete Marshall-Olkin Generalized exponential, discrete Gompertz-G-exponential, discrete Weibull, discrete inverse Weibull, exponentiated discrete Weibull, discrete Rayleigh, and new discrete Lindley. The probability mass function and the hazard rate function are addressed. Discrete models are discussed based on the maximum likelihood estimates for the parameters. A numerical analysis uses the regular count of new casualties in the countries of Angola,Ethiopia, French Guiana, El Salvador, Estonia, and Greece. The empirical findings are interpreted in-depth.

Statistical modeling of annual highest monthly rainfall in Zimbabwe.

The first statistical analysis of maximum rainfall in Zimbabwe is provided. The data are from 103 stations spread across the different climatic regions of Zimbabwe. More than 90% of the stations had at least 50 years of data. The generalized extreme value distribution was fitted to maximum rainfall by the method of maximum likelihood. Probability plots, quantile plots and Kolmogorov-Smirnov tests showed that the generalized extreme value distribution provided an adequate fit for all stations. The vast majority of stations do not exhibit significant trends in rainfall. Twelve of the stations exhibit negative trends and three of the stations exhibit positive trends in rainfall. Estimates of return levels are given for 2, 5, 10, 20, 50 and 100 years.

Re-visiting the COVID-19 analysis using the class of high ordered integer-valued time series models with harmonic features.

The COVID-19 series is obviously one of the most volatile time series with lots of spikes and oscillations. The conventional integer-valued auto-regressive time series models (INAR) may be limited to account for such features in COVID-19 series such as severe over-dispersion, excess of zeros, periodicity, harmonic shapes and oscillations. This paper proposes alternative formulations of the classical INAR process by considering the class of high-ordered INAR models with harmonic innovation distributions. Interestingly, the paper further explores the bivariate extension of these high-ordered INARs. South Africa and Mauritius' COVID-19 series are re-scrutinized under the optic of these new INAR processes. Some simulation experiments are also executed to validate the new models and their estimation procedures.

Socio-economic and demographic impacts on the full awareness of the methods for controlling/preventing the spread of COVID-19 among social media users in some African countries at the onset of the pandemic.

OBJECTIVE: In Africa, most countries continue to battle COVID-19 with cases of newly infected still being recorded. In this note, we investigate how socioeconomic and demographic factors affected individuals awareness on the methods for controlling/preventing the spread of COVID-19 in some parts of Africa at the onset of the pandemic. RESULTS: Based on regression modelling, we find that having full awareness does not depend on religious affiliation. Men, urban dwelling, holding bachelors or higher degrees, operating multiple social media accounts or being employed are associated with having full awareness of the recommended practices for the prevention and control of COVID-19 at the early stage of the pandemic. No occupation, business or older people are associated with not having full awareness.

The impact of socio-demographic factors on the survival of cancer patients in Zimbabwe.

We provide a survival analysis of cancer patients in Zimbabwe. Our results show that young cancer patients have lower but not significant hazard rate compared to old cancer patients. Male cancer patients have lower but not significant hazard rate compared to female cancer patients. Race and marital status are significant risk factors for cancer patients in Zimbabwe.

Count regression models for COVID-19.

At the end of 2019, the current novel coronavirus emerged as a severe acute respiratory disease that has now become a worldwide pandemic. Future generations will look back on this difficult period and see how our society as a whole united and rose to this challenge. Many reports have suggested that this new virus is becoming comparable to the Spanish flu pandemic of 1918. We provide a statistical study on the modelling and analysis of the daily incidence of COVID-19 in eighteen countries around the world. In particular, we investigate whether it is possible to fit count regression models to the number of daily new cases of COVID-19 in various countries and make short term predictions of these numbers. The results suggest that the biggest advantage of these methods is that they are simplistic and straightforward allowing us to obtain preliminary results and an overall picture of the trends in the daily confirmed cases of COVID-19 around the world. The best fitting count regression model for modelling the number of new daily COVID-19 cases of all countries analysed was shown to be a negative binomial distribution with log link function. Whilst the results cannot solely be used to determine and influence policy decisions, they provide an alternative to more specialised epidemiological models and can help to support or contradict results obtained from other analysis.