|
|
American Journal of Mathematics and Statistics
Number of Followers: 9  Open Access journalISSN (Print) 2162-948X - ISSN (Online) 2162-8475 Published by SAP  [105 journals]
|
- Handling Missing Values in Covariate for Modeling Count Data with over
Dispersion and Zero Inflation
Abstract: Publication year: 2023Source: American Journal of Mathematics and Statistics, Volume 13, Number 1Rajibul Mian, Sudhir PaulThe problem of regression analysis of count response data having information on some covariates missing may arise in some practical applications. Further complications, such as, over-dispersion and zero-inflation in the count responses, may also arise. In this paper we develop estimation procedure for the parameters of a zero inflated over/under dispersed count response model in the presence of missing covariates. A zero-inflated negative binomial model with missing covariate information is used. Obtaining maximum likelihood estimates by direct use of the log-likelihood involves multiple numerical integration. To avoid this we develop a weighted expectation maximization algorithm. A simulation study is conducted to investigate the properties of the estimates, in terms of bias, variance, mean squared errors (MSE) and coverage probability (CP). Further simulations are also conducted to study Robustness of the procedure for count data following other over-dispersed models, such as the log-normal mixture of the Poisson distribution. An example and a discussion are given.
- Approximating Non-Asymptoticalness, Skew Heteroscedascity and
Geo-spatiotemporal Multicollinearity in Posterior Probabilities in
Bayesian Eigenvector Eigen-Geospace for Optimizing Hierarchical
Diffusion-Oriented COVID-19 Random Effect Specifications Geosampled in
Uganda
Abstract: Publication year: 2023Source: American Journal of Mathematics and Statistics, Volume 13, Number 1Benjamin G. Jacob, Ricardo Izureta, Jesse Bell, Jeegan Parikh, Denis Loum, Jesse Casonova, Tracy Gates, Kayleigh Murray, Leomar White, Jane Ruth AcengThis paper presents two space-time model specifications, one based upon the generalized linear mixed model (GLMM), and the other upon Moran eigenvector space-time filters. We identify optimization algorithms to fit a COVID-19 regression model to a training dataset. of non-asymptotical, multicollinear, skew heteroscedastic, estimator and other non-normalities due to violations of regression assumptions We did so to learn more about how regression functions can characterize geo-spatiotemporally, spilled over, hierarchical diffusion of the viral infection in Uganda at the sub-county district-level. Our objective was to predictively prioritize and target, of hyper/hypo-endemic transmission variables. A Moran spatial filtering technique was employed which performed an eigenfunction, second order, eigen-spatial filter eigendecomposition of the random effects (REs) in varying, temporally dependent, georeferenced, diagnostically stratified, clinical, environmental, and socio-economic, endemic, transmission-oriented determinants which rendered (SSRE) and spatially unstructured (SURE) components. The RE model incorporated synthetic eigen-orthogonal eigenvectors derived from a geographic connectivity matrix to account for SSRE and SURE in standardized z scores stratified by multi-month, viral, infection yield, due to geo-spatiotemporal, spill-over, hierarchical diffusion of the virus at the sub-county, district-level. We calculated the conditional probabilities and derived the conditional distribution functions for the regressed diagnostic determinants including the probability density function, the cumulative density function, and quantile function. A Poisson random variable mean response specification was written as follows:
where esitk and eHith respectively were the ith elements of the K < NT and H < NT selected eigenvectors and Estk and EHthwere extractable from the doubly-centered space-time 
and 
The expectation attached to the equation, i.e., RE ≡ SURE was satisfied, with both having trivial SSRE components. In the Bayesian context, the SSRE component was modelled with a conditional autoregressive specification which captured residual, zero autocorrelation (i.e., geographic chaos), non-homoscedastic, asymptotical non-normality and multicollinearity in the georeferenced, aggregation/non-aggregation-oriented, COVID-19, specified, diagnostically stratified, prognosticator, clustering propensities. The model’s variance implied a substantial variability in the prevalence of COVID-19 across districts due to the hierarchical diffusion of the virus. Site-specific, semi-parametric eigendecomposable, eigen-orthogonal, eigen-spatial filters are useful in revealing the influence of non-normality [e.g., heterogeneity of variances] in diagnostic, COVID-19 variables due to violations of regression assumption and hence are more accurate in prediction of georeferenceable, hyper/hypo-endemic, sub-county, transmission-oriented district-level geolocations compared with a global model in which the non-homogenous erroneous estimators and their evidential uncertainty-oriented probabilities do not vary across Bayesian eigenvector eigen-geospace.
- Determination of Nutritional Status of Children by Their Body Mass Index
Using Percentile Tables
Abstract: Publication year: 2022Source: American Journal of Mathematics and Statistics, Volume 12, Number 2Adeyemo S. O., Ofomata A. I. O., Okereke I. C.This is a descriptive study carried out to determine the nutritional status of children within the ages of four(4) to ten (10) years using their body mass index(BMI). Body Mass Index (BMI) is a statistical parameter used to determine the nutritional status/body weight efficiency of individuals, and it has been used in many countries for assessment of underweight, healthy weight, overweight and obesity in children and adults. The prevalence of obesity in children is increasing and is recognized as a risk indicator of cardiovascular disease in adulthood. The weights and heights of 600 (300 males and 300 females) sampled children were measured and their BMI was calculated as weight(kg)/height2 (m2). under weight, healthy weight, over weight and obese children were identified using charts from pooled internationally accepted data age and sex specific cut -off points for BMI. The BMI ranges from 09.25kg / m2. To 28.20Kg/m2 with a mean BMI of 15.02 kg/m2. The mean BMI for males was 15.33kg/m2 and that for females 14.71kg/m2. The prevalence of Underweight, Healthy weight, overweight and obesity were 16.33, 64.34%, 12% and 7.33% respectively. More males were significantly malnourished than females. Most children had BMI within the normal range. The prevalence of malnourishment among children though predominantly low should be taken seriously, especially as it appears to be associated with improving socioeconomic status. School health education (physical activity and nutritional education) is recommended as preventive measures.
- Markov Switching Autoregressive Modelling of the COVID-19 Daily Cases and
Deaths in Nigeria
Abstract: Publication year: 2022Source: American Journal of Mathematics and Statistics, Volume 12, Number 2Benson T. I., Biu E. O., Nwakuya M. T.This article modeled the daily COVID-19 infected cases and deaths of Nigeria using a Markov switching model. Structural breaks and Stationarity of the daily COVID-19 cases and deaths series were investigated. Unit root and unit root structural break tests were applied where evidence of breaks exists. The results show that each of the series was found to be a nonlinear and nonstationary series with evidence of a structural break. The results of the unit root tests in the presence of structural breaks indicated that each of the series was two significant wave changes. Consequently, a Markov switching AR (MSM(2)-AR(1)) model with two regimes was fitted to the data having established its suitability in modelling the series. Finally, a transition probability matrix between the expected number of COVID-19 infected cases and death cases was obtained.
- Mover-Stayer Analysis of the Movement Pattern of Nigeria's External
Reserves
Abstract: Publication year: 2022Source: American Journal of Mathematics and Statistics, Volume 12, Number 1Yusuf J. Adams, Mohammed Bapparu, Emmanuel J. WayaExternal Reserve is a major monetary indicator, as it enables the Central Banks to intervene in the foreign exchange market and helps cushion the economy from external shocks. A lot of work had been done, in terms of analyzing the effect or otherwise of External Reserves on various economic indicators in Nigeria. However, attention has not been given to the pattern of movement of this important indicator over the years. This paper analyzed the movement pattern of this important monetary indicator using the Mover-Stayer technique advanced by Adams and Abdulkadir (2018), using data collected from the Central Bank of Nigeria Database over the period 2001 – 2020. The data was classified and coded into four (4) groups based on the amount that gives three months import cover. The proportions of stayers to various coded groups as well as the individual-level transition matrix were estimated.
- Algebraic Points of Given Degree on the Affine Curve
Abstract: Publication year: 2022Source: American Journal of Mathematics and Statistics, Volume 12, Number 1El Hadji Sow, Moussa Fall, Oumar SallIn this work, we determine the set of algebraic points of given degree over
on the curve of affine equation 
This note extends a result of Booker, Sijsling, Sutherland, Voight and Yasak in [1] who gave a description of the set of 
-rational points i.e the set of points of degree one over 
on this curve.
- Method of Estimating the Transition Matrix (M) of the Mover-Stayer Model
When Rate of Transition Follows Negative Binomial Distribution
Abstract: Publication year: 2022Source: American Journal of Mathematics and Statistics, Volume 12, Number 1Yusuf J. Adams, Sauta S. Abdulkadir, Hamidu U. WaniyosMotivated by the work of Spilerman (1972) and that of Johnson, Kotz and Kemp (1992), on extension of the Mover-Stayer model, Adams and Abdulkadir (2018) assumed negative binomial distribution for
to model rate of transition in Poisson distribution, which gave the Polya-Aeppli distribution as a mixture. However, that paper did not specify a method or derive an expression for estimating the transition matrix M. This paper attempts to provide a method of estimating the transition matrix M, to compliment the work earlier done by Adams and Abdulkadir (2018). In addition, an attempt was made to obtain an estimate of the stayer population. The obtained expressions were tested using simulated data adopted from Spilerman (1972).
- The Result of a Square Root Transformation on the Error Part of the
Additive Time Series Model
Abstract: Publication year: 2021Source: American Journal of Mathematics and Statistics, Volume 11, Number 4C. A. Igbo, E. L. OtuonyeThe square root transformation of the error component of the additive time series model was studied. The distribution of the transformed error component was established and shown that it is a proper probability density function. The properties of the distribution were investigated. It was shown that the mean of the transformed series
is equal to one while the mean of the original series = 0 for 
. Also, the variance of the transformed was established and given as 
and is four times that of the original series for 
to one decimal place. The transformed series is normally distributed for 
.
- The Quadratic Equation Concept
Abstract: Publication year: 2021Source: American Journal of Mathematics and Statistics, Volume 11, Number 3Ashwannie HarripersaudThe purpose of this essay is to act as a supplement for students who wish to reinforce their knowledge of the quadratic formula. It is not intended to be used as a primary source of education. If so, it should be used in collaboration with an expert of mathematics. This essay focuses primarily on the ways a quadratic equation can be solved. This includes an explanation of factoring, completing the square, the quadratic formula, and references to graphical approaches and analysis.
- Maximum Entropy Estimation: Agronomic Dataset
Abstract: Publication year: 2021Source: American Journal of Mathematics and Statistics, Volume 11, Number 3Raymond Bangura, Sydney JohnsonWe provide a generalized maximum entropy method and its application to the Agronomic dataset. Errors of deviation are shown with the analysis of variance on the entropy method. Multi-collinearity is one of the major problems of regression analysis. Based on the maximum entropy method, we gave a better estimate than the traditional robust regression of four independent variables from an Agronomic dataset. From the generalized maximum entropy method, we showed the relationship between the dependent and independent variables. Also, we provided a diagnostic fit for the dependent variable to support the theoretical analysis.
