Statistics

Moderated mediation has been proven to be one of the useful techniques in providing powerful analysis in many research areas such as social science, statistics, marketing, health science and others. By using secondary data obtained from Trends In Mathematics and Science Study (TIMSS), moderated mediation analysis is used to determine the significance difference of direct effect and total effect including indirect effect of exogenous latent constructs toward endogenous latent construct through mediator latent construct between moderator; male and female samples. From the Moderation Analysis, it is found that there is no significant difference between male and female samples in the direct effect of all exogenous latent constructs toward endogenous latent construct. The same result obtained in Moderated Mediation Analysis where there is no significant difference between male and female samples in the total effect including indirect effect from all exogenous latent constructs toward endogenous latent construct through mediator latent construct.

This study was carried out to examine survey responses across various levels of response predictors in some selected communities in oyo town, Oyo State, Nigeria. The design for this study was a two-stage stratified random sampling scheme. A Sample of 750 households was randomly selected in fifteen Enumeration Areas in Oyo town. The data were collected by interviewer-administered questionnaire and predictors of response were extracted for the verification of response rates at various levels of these predictors. Out of the 750 respondents that were interviewed in each of the five waves, 545, 615, 610, 615, 605 responded to survey questions respectively. The maximum number of visits considered for this research work is five per wave and after the fifth visits, respondents were regarded as non response. The response rates from the following predictors:- Females, those that were living with their spouse, those that were interviewed with English language, respondents at the middle age (50-79 years), those that are familiar with the interviewer and tenants were observed to be high. Also, the response rates increases from first visit to the fourth visits and at the fifth visit, it declined. We also observed that the more the number of years a respondent has spent in his/her community, the more they response to survey questions.

In this paper, we have considered the problem of estimating the population mean of study character using mean square error by double sampling the non-respondents. Two generalized estimators for estimating the population mean using auxiliary character under two different cases are proposed. Further the problem has been extended to the wider classes of estimators, which include several generalized estimators as a particular member. The bias, mean square error and optimum property of the proposed classes of estimators have been obtained under different cases. The efficiency of the proposed classes of estimators has also been shown through the theoretical and empirical studies. 

The study of stochastic phenomena has increased dramatically and intensified research activity in this area has been stimulated by the need to take into account random effects in complicated dynamical systems. Dynamical systems are ubiquitous and are considered to be stochastic processes. In this study, a nonlinear dynamical system was modeled as a solution to an Ito stochastic differential equation . Where denotes a Wiener or Brownian motion process while and are deterministic functions. The Ito Stochastic Differential Equation was applied to characterize the important functional of the solution process in some intervals [0,t],X(t) which satisfies the integral equation, X(t)=X(0)+?_0^t??f(s,X(s))ds?+?_0^t??g(s,X(s) )dW(s)?. The solution of the integral equation is a Lagenvin equation which is an Ornstein-Uhlenbeck (O-U) process dX_t=?(?-X_t )dt+?dW_t. The O-U process which is a Gaussian process was related to the world of time series analysis. The model was applied to Nigerian monetary exchange rate and compared with the existing models of monetary exchange rate. R package and the Akaike Information Criteria (AIC) were used to provide the model of best fit for the Nigerian monetary exchange rate as an autoregressive moving average of order one which is given to be? S?_t=0.4287S_(t-1)+?0.2099e?_(t-1)+e_t. The results obtained revealed that the structural diffusion model approach gives a first-order autoregressive moving average process in continuous time with differentiation in continuous time corresponding to differencing in discrete time. The derived structural diffusion model has the least AIC value of 1482.61 as compared to the AIC value of 2198.86 from the existing diffusion and normal models. Keywords: Nonlinear Model, Dynamical System, Diffusion Model,

This work examined the efficiencies of Ordinary Least Squares (OLS) and Seemingly Unrelated Regression (SUR) estimators in lagged and unlagged models. Literature has shown gain in efficiency of SUR estimator over OLS estimator when the errors are correlated across equations. This paper studied the efficiencies of these estimators in a lagged and unlagged models and also sought a comparative study of these estimators in both models.Data was simulated for sample sizes 50, 100 and 1000 with 5000 bootstrapped replicates in each case with the predictors having Gaussian distribution. Results from the study showed that both estimators were efficient in each model with the SUR estimator being consistently more efficient than the OLS estimator as the sample size increased. On the assessment of the models, the unlagged model was found to be more efficient than the lagged model in small sample but converged as sample size increased.

Nigeria is classified as a mixed economy emerging market, and has already reached middle income status according to the World Bank, with its abundant supply of natural resource, well developed financial, legal, communications, transport sectors and stock exchange which is the second largest in Africa. The main purpose of this research is to build a model that can capture the best variables that predict the Gross Domestic Product (GDP) of Nigeria. Correlation matrix was used to know the degree of relationship that exists between the pairs of predictors of GDP. The principal component analysis was employed to reduce the multidimensional data. Scree plot was used to determine the spread of the trend of the components and bi plot was used to determine the degree of closeness of Agriculture, oil Export, External Reserves, Exchange Rate, Transportation, Education, and Communication. There is a strong relationship between pairs of Agriculture, oil Export, External Reserves, Exchange Rate, Transportation, Education, and Communication. The proportion of variance accounted for by the first component is 92%. This implied that only component 1 is sufficient to explain GDP. The Scree plot showed that the best component is component 1. The bi plot showed that Agriculture, oil Export, External.Reserves, Exchange.Rate, Transportation, Education, and Communication are closely related and stand as good predictors of GDP. Keyword: Gross Domestic Product, Principal Components, Bi plot, Scree plot

Abstract Thomas Robert Malthus Theory of population highlighted the potential dangers of over population. He stated that while the populations of the world would increase in geometric proportions, the food resources available for them would increase in arithmetic proportions. This study was carried out to find the trend, fit a model and forecast for the population growth rate of Nigeria.The data were based on the population growth rate of Nigeria from 1982 to 2012 obtained from World Bank Data (data.worldbank.org). Both time and autocorrelation plots were used to assess the Stationarity of the data. Dickey-Fuller test was used to test for the unit root. Ljung box test was used to check for the fit of the fitted model. Time plot showed that the random fluctuations of the data are not constant over time. There was an initial decrease in the trend of the growth rate from 1983 to 1985 and an increase in 1986 which was constant till 1989 and then slight fluctuations from 1990 to 2004 and a general increase in trend from 2005 to 2012. There was a slow decay in the correlogram of the ACF and this implied that the process is non stationary. The series was stationary after second differencing, Dickey-Fuller = -4.7162, Lag order = 0, p-value = 0.01 at ?= 0.05. The p-value (0.01) and concluded that there is no unit root i.e the series is stationary having d=2. Correlogram and partial correlogram for the second-order differenced data showed that the ACF at lag 1 and lag 5 exceed the significant bounds and the partial correlogram tailed off at lag 2.The identified order for the ARIMA(p,d,q) model was ARIMA(2,2,1). The estimate of AR1 co-efficient =1.5803 is observed to be statistically significant but the estimated value does not conforms strictly to the bounds of the stationary parameter hence was excluded from the model. =-0.9273 is observed to be statistically significant and conformed strictly to the bounds of the stationary parameter , hence was maintained in the model. The estimate of MA1 co-efficient = - 0.1337 was observed to be statistically significant conformed strictly to the bounds of the parameter invertibility. For ARIMA (2, 2, 0) the estimate of AR1 co-efficient =1.5430 was observed to be statistically significant and not conformed strictly to the bounds of the parameter stationary, hence excluded from the model. The estimate of AR 2 co-efficient =-0.9000 is observed to be statistically significant and conformed strictly to the bounds of the parameter stationary, hence retained in the model. The ARIMA (2, 2, 0) is considered the best model. It has the smallest AIC. The Ljung test showed that residuals are random and implies that the model is fit enough for the data. The forecast Arima function gives us a forecast of the Population Growth Rate in the next thirty eight (38) years, as well as 80% and 95% prediction intervals for those predictions i.e up to 2050. Keywords: Modelling, ARIMA Model, Parameter, Dickey-Fuller, Stationarity

The ordinal regression is a method that is used to robust the model when dependent variable is ordinal and Independent variables may be dichotomous, polytomous, and continuous or combination of these. Ordinal logistic regression is used to predict the “odds” of having a lower or a higher value for dependent variable (y), based on independent variable (x). In practice, the frequently used type of model is a proportional odds model in ordinal logistic regression. HIV testing is necessary for preventing and reducing the HIV transmission. However, there are various Socio-demographic and HIV related behavior factors contribute the high or low HIV testing in general population and high risk groups. Intend of this study find out the important factors of the HIV testing in Injecting drug users (IDUs) patients. The ordinal logistic regression model makes assumptions about the nature of the relationship between the order response variable HIV testing Methods: Total 139 IDUs patients’ collect the information for this research based on specific questioner from the district Kamur in Bihar. In study, Ordinal logistic regression analysis to determine the factors which are considered to be a significant contributor in HIV testing. The ordinal logistic regression model was used to build models for dependent variable HIV testing and independent variables which are Age, Marital Status, Education, Occupation, Stigma, Income, STI/STD problems, Needle injecting sharing and HIV information. Results: In this research apply the proportional odds model for confirm the applicability of the ordinal logistic model. We determine the all parameter the significant of the model. We found that Needle sharing, Abscess problem, Abuse, Heard about STI, HIV, Income, HIV knowledge, HIV transmission through multiple partners shows significant contribution to IDUs patient for HIV testing. Conclusion: This study has made an attempt to recognize the predictors of HIV testing for injecting drug users by developing an ordinal logistic regression model.

Nowadays organizations are starting to realize the importance of using more data in order to support decision for their strategies. The size of data in world is growing day by day. Data is growing because of vast use of internet, smart phone and social network. Big data is a collection of data sets which is very large in size as well as complex. Generally size of the data is Petabyte and Exabyte. Traditional database systems are not able to capture, store and analyze this large amount of data. As the internet is growing, amount of big data continue to grow. Big data analytic provide new ways for businesses and government to analyze unstructured data. Nowadays, Big data is one of the most talked topic in IT industry. It is going to play important role in future. Big data changes the way that data is managed and used. Some of the applications are in areas such as healthcare, defense, traffic management, banking, agriculture, retail, education and so on. Organizations are becoming more flexible and more open. New types of data will give new challenges as well.

In this paper we work on Frechet distribution with Bayesian paradigm. Posterior distribution is obtained by using Uniform, Jeffreys and generalization of non-informative priors. We use the quadrature numerical integration to solve the posterior distribution. Bayes estimator and their risk have been obtaining four loss functions. The performances of Bayes estimators are compared by using Monte Carlo simulation study.