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Demonstrating the Performance of Accelerated Failure Time Model Over Cox-PH Model of Survival Data Analysis with Application to HIV-Infected Patients Under HAART
Issue:
Volume 8, Issue 6, November 2019
Pages:
193-202
Received:
3 May 2019
Accepted:
24 October 2019
Published:
31 October 2019
Abstract: Human Immunodeficiency Virus (HIV) is a virus that kills CD4 cells. These CD4 cells are white blood cells that fight infection. CD4 count is like a snapshot of how well our immune system is functioning. Studying the way of CD4+ count over time provides an insight to the disease evolution. This study was considering the data of HIV/AIDS patients who were undergoing Antiretroviral Therapy in the ART clinic of Menellik II Referral Hospital, Addis Ababa, Ethiopia, during the period 1st January 2014 to 31st December 2017. For separate survival model log-logistic model is more appropriate for the survival data than other parametric models. Therefore; functional status and regimen class are significant covariates in determining the hazard function patients. Log rank and Wilcoxon tests showed that the significant difference in survival situation among the categorical variables selected for this study sex, marital status, functional status, WHO-clinical stages and regimen class subgroups. But, there was no significant difference in the time-to-event between subgroups of sex, Marital Status and WHO clinical Stage, while, Regimen Class and Functional Status there was a significant difference in the time-to-event between subgroups.
Abstract: Human Immunodeficiency Virus (HIV) is a virus that kills CD4 cells. These CD4 cells are white blood cells that fight infection. CD4 count is like a snapshot of how well our immune system is functioning. Studying the way of CD4+ count over time provides an insight to the disease evolution. This study was considering the data of HIV/AIDS patients who...
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Errors of Misclassification Associated with Edgeworth Series Distribution (ESD)
Awogbemi Clement Adeyeye,
Onyeagu Sidney Iheanyi
Issue:
Volume 8, Issue 6, November 2019
Pages:
203-213
Received:
2 March 2018
Accepted:
30 March 2018
Published:
8 November 2019
Abstract: This study investigates the errors of misclassification associated with Edgeworth Series Distribution (ESD) with a view to assessing the effects of sampling from non-normality. The effects of applying a normal classificatory rule when it is actually a persistent non-normal distribution were examined. These were achieved by comparing the errors of misclassification for ESD with ND using small sample sizes at every level of skewness factor. The simulation procedure for the experiment of the study was implemented using numerical inverse interpolation method in R program to generate a uniformly distributed random variable N. A configuration size of 1000 was obtained for the two training samples drawn at every level of skewness factor (λ3), in the range (0.00625, 0.4). This was repeated for different small sample sizes by comparing errors of misclassification of ESD with ND. The simulation results showed that the optimum probabilities of misclassification by ESD: (E12E) decreases and (E12E) increases, as the skewness factor (λ3) increases. The optimum total probability of misclassification is stable as λ3 also increases. The probability of misclassification E12E ≥E12N and E21E ≥E21N at every level of λ3. Thus, the total probabilities of misclassification are not greatly affected by the skewness factor. This asserts that the normal classification procedure is robust against departure from normality.
Abstract: This study investigates the errors of misclassification associated with Edgeworth Series Distribution (ESD) with a view to assessing the effects of sampling from non-normality. The effects of applying a normal classificatory rule when it is actually a persistent non-normal distribution were examined. These were achieved by comparing the errors of m...
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Determine Joint Factors that Affect Maternal Weight and Body Mass Index Among Pregnant Women in Ethiopia: A Bi-variate Analysis
Melkamu Ayana Zeru,
Kindu Kebede Gebre
Issue:
Volume 8, Issue 6, November 2019
Pages:
214-220
Received:
5 August 2019
Accepted:
15 October 2019
Published:
8 November 2019
Abstract: Introduction: A low maternal body mass index and sub-optimal weight gain during pregnancy are long recognized risk factors for delivery of infants too small for gestational age, low birth weight as well as to increase the risk of subsequent obesity and hypertension in the off- spring. Maternal body mass index and maternal weight is positively associated with infant obesity risk. The main objective of this research was to determine the determinants of maternal body mass index and maternal weight simultaneously based on Ethiopia demographic health survey 2016 which was implemented in statistical package R. Methodology: Cross sectional study design was used from Ethiopia demographic health survey 2016. Bi-variate linear regression model was used to determine the factors that affect maternal body mass index and maternal weight simultaneously. Result: The bi-variate analysis of maternal pregnancy weight and body mass index identified that the co-variate husband educational level, preferred waiting time for birth, region, family size, frequency of watching television, maternal height, desire for more children and number of tetanus injections before pregnancy were statistically associated with maternal pregnancy weight. Moreover, educational level of husband, preferred waiting time for birth, region, family size, desire for more children, frequency of watching television and number of tetanus injections before pregnancy were statistically significant for maternal pregnancy body mass index in Ethiopia (p≤0.05). Conclusion: The risk of over pregnancy weight and body mass index increased when parent prefer high number of waiting time to birth another child in Ethiopia. In addition the risk of over pregnancy weight and body mass index increased when mother received more tetanus injection during pregnancy.
Abstract: Introduction: A low maternal body mass index and sub-optimal weight gain during pregnancy are long recognized risk factors for delivery of infants too small for gestational age, low birth weight as well as to increase the risk of subsequent obesity and hypertension in the off- spring. Maternal body mass index and maternal weight is positively assoc...
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Modeling Mortality Rates Using Heligman-Pollard and Lee-Carter in Nigeria
Yahaya Haruna Umar,
Ugboh Joshua Chukwudi
Issue:
Volume 8, Issue 6, November 2019
Pages:
221-239
Received:
25 April 2019
Accepted:
29 September 2019
Published:
13 November 2019
Abstract: In recent years the need for accurate mortality statistics has been emphasized by researchers in planning, analyzing, monitoring and projection of health situations in the country. It helps the government and other health agencies initiate various programs that can improve life expectancy especially in developing countries like Nigeria. Given the impact of mortality rates on the population size, structure, social security system, life insurance and pension (from actuarial point of view) there is need to understand how mortality patterns change with time. According to past studies the Heligman-Pollard (Henceforth HP) model and Lee-Carter (Henceforth LC) model have been widely accepted and use by researchers in forecasting future mortality. In this study both models were applied to Nigerian data with the objective to investigate the accuracy of their performances by comparing their assumptions. The LC model parameters were estimated based on the singular value decomposition technique (SVD), while HP model parameters were estimated using nonlinear least squares method. Autoregressive Integrated Moving Average (ARIMA) procedure was applied to acquire to forecasted parameters for both models. To investigate the accuracy of the estimation, the forecasted results were compared based on the mean absolute percentage error (MAPE). The results indicate that both models provide better results for female population. However, for the elderly female population, HP model seems to overestimate to the mortality rates while LC model seems to underestimate to the mortality rates. Although the HP model does not seem to follow the pattern of the actual mortality rates, after further analysis was carried out it was discovered that the HP model gave a better forecast than the Lee-Carter model. Based on the HP model the forecasted probabilities of death were used to construct an abridged life table for males and females and the life expectancy at e0 and e75 were obtained. From our results we see that males experience higher life expectancy than females due to the mortality rates experienced by both sexes. Given the level of mortality rate especially in developing countries like Nigeria, the study therefore recommends the need for a vital registration system that could continuously and reliably collect information because it is well known that incomplete data affect the performance of a model to forecast. To ascertain level and pattern of mortality rate especially in adult, parameterization model especially the HP model should be considered because of it lesser errors, with the view of achieving a robust forecasting model that could improve the understanding of the pattern of general mortality rate and how it affects life expectancy level in the country.
Abstract: In recent years the need for accurate mortality statistics has been emphasized by researchers in planning, analyzing, monitoring and projection of health situations in the country. It helps the government and other health agencies initiate various programs that can improve life expectancy especially in developing countries like Nigeria. Given the i...
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A Statistical Comparison of NRHM 2007-08 and 2012-13 Survey Data
Vikram Singh,
Santosh Kumar Gupta,
Jagdish Prasad
Issue:
Volume 8, Issue 6, November 2019
Pages:
240-245
Received:
11 June 2019
Accepted:
15 August 2019
Published:
15 November 2019
Abstract: Important of health in the process of economic and social development and improving the quality of life of our citizens, the Government of India has launched the National Rural Health Mission. District level Household and Facility survey DLHS-3 and DLHS-4 conducted by Ministry of Health and family Welfare of New Delhi and International Institute for Population Science of Mumbai in 2007-08 and 2012-13 for Rajasthan. These surveys provide effective health care to rural population in the state, which has poorer health outcomes and inadequate public health infrastructure and manpower. The primary focus of the mission is the improve access of rural people, especially women and children, to equitable and affordable primary health care. In this paper the infrastructure facility in SHC, PHC and CHC has been increased from 2007-08 to 2012-13 NRHM DLHS is assesses through statistical analysis. Facility survey is carried out for the central and state government in evaluation monitoring and planning strategies.
Abstract: Important of health in the process of economic and social development and improving the quality of life of our citizens, the Government of India has launched the National Rural Health Mission. District level Household and Facility survey DLHS-3 and DLHS-4 conducted by Ministry of Health and family Welfare of New Delhi and International Institute fo...
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Estimation of CPI of Some Sub-sahara African Countries: Panel Data Approach
Oyekunle Janet Olufunmike,
Ayoola Joshua Femi,
Oyenuga Iyabode Favour,
Masopa Adekunle Nurudeen,
Adesiyan Adefowope Abdul Azeez
Issue:
Volume 8, Issue 6, November 2019
Pages:
246-252
Received:
13 July 2019
Accepted:
31 October 2019
Published:
15 November 2019
Abstract: One of the economic indicators that are necessary to provide information on the state and progress of country is the Consumer Price Index (CPI) which measures changes in the price of goods and services over a certain period of time. An effective monetary policy depends on the ability of economists to develop a reliable model that could understand the ongoing economic processes and predict future developments. Hence, this study is aimed at estimating CPI (a component of Inflation) in 20 Sub–Sahara African (SSA) countries in relation to Broad Money (BM), Export Rate (EXP), Gross Domestic Product (GDP) and Private Consumption Expenditure (PCE) using panel data approach. The data was extracted from the World Bank Data Bank for a period of 30 years (1987-2016). The Fixed Effect Model (FEM) was employed and the model summary was computed using the panel least squares. The Variance Inflation Factor (VIF) was used to test for the presence of multicollinearity. The result of the analysis shows that the CPI for SSA countries ranges from 0.0007% to 298.51% (2010=100) with an average of 59.76%. All the predictors included in estimating the CPI have significant effect at 5% level except the GDP. The estimated panel regression equation is CPIit=71.4449-0.1735BMit-0.3309EXPit+7.4338e-12GDPit+1.1335e-10PCEit. The estimated coefficient of determination is 0.853 which means that 85.3% of the total variation in CPI can be accounted for by the variations in the macroeconomic variables included. The VIF for all the variables is less than 3.o meaning that there is no sign of multicollinearity and therefore, there is no correlation among the predictors. It was concluded that the FEM estimated can be used to assess the behavior of the CPI in the nearest future. Moreover, 85.3% of the variations in CPI can be explained by the economic variables used as independent variables. It is recommended that efforts should be geared towards improving the input of these variables in the economy such that appropriate relationship will exist between them and the CPI in the SSA nations.
Abstract: One of the economic indicators that are necessary to provide information on the state and progress of country is the Consumer Price Index (CPI) which measures changes in the price of goods and services over a certain period of time. An effective monetary policy depends on the ability of economists to develop a reliable model that could understand t...
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Asymptotic Properties of Optimized Type CVaR Estimator for NA Random Variables
Shanchao Yang,
Yuting Wang,
Xin Yang,
Xiutao Yang
Issue:
Volume 8, Issue 6, November 2019
Pages:
253-260
Received:
8 October 2019
Accepted:
9 November 2019
Published:
25 November 2019
Abstract: VaR and CVaR are important risk measures, which are widely used in finance, economy, insurance and other fields. However, VaR is not a coherent risk quantity, and it is not sufficient to measure tail risk. CVaR (also known as expected shortfall, ES) is a coherent risk measure, and it makes up for the defect that VaR is not enough to measure tail risk. Therefore, CVaR has been paid more and more attention in both application and theory fields. Rockafellar and Uryasev (2000) and Trindade et al (2007) proposed an optimized type CVaR estimator and studied some asymptotic properties of the estimator. Since then, some scholars have discussed the properties of the estimator in the cases of ρ-mixing, φ-mixing and α-mixing. In this paper, we shall study the asymptotic properties of the optimized type CVaR estimator in the case where the samples are NA random variables. The consistency and the asymptotic normality of the optimized type CVaR estimator and their corresponding convergence rates are obtained. The convergence rates of estimation are n-1/2 or near to n-1/2. These results also establish the asymptotic relations of the optimized type CVaR estimator and the common CVaR estimator. And their deviation converges almost surely to 0 at the rate of n-1/2.
Abstract: VaR and CVaR are important risk measures, which are widely used in finance, economy, insurance and other fields. However, VaR is not a coherent risk quantity, and it is not sufficient to measure tail risk. CVaR (also known as expected shortfall, ES) is a coherent risk measure, and it makes up for the defect that VaR is not enough to measure tail ri...
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Applying Survival Analysis to Telecom Churn Data
Melik Masarifoglu,
Ali Hakan Buyuklu
Issue:
Volume 8, Issue 6, November 2019
Pages:
261-275
Received:
12 February 2018
Accepted:
5 March 2018
Published:
2 December 2019
Abstract: In competitive telecommunication environment, it is imperative to maintain an effective customer retention strategy even while mobile service operators attracting new customers. Not only acquiring new customers costly process, but successful customer retention helps build brand loyalty and good business reputation. Motivated by real mobile service operator data set, we designed and proposed a solution to employ survival analysis technique that estimates customers’ survivals and hazards. We aim to examine the impact of: campaign, tariff, tenure, age, auto-payment on survival times and hazards. After hazard ratios and survival experiences determined for each predictor, results enable mobile service operator to target the right customers to incentivize so that they can stay with their current operator. Proactive actions triggered by the results of the survival model is key to customer retention.
Abstract: In competitive telecommunication environment, it is imperative to maintain an effective customer retention strategy even while mobile service operators attracting new customers. Not only acquiring new customers costly process, but successful customer retention helps build brand loyalty and good business reputation. Motivated by real mobile service ...
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Volatility of Internally Generated Revenue and Effects of Its Major Components: A Case of Akwa Ibom State, Nigeria
Usoro Anthony Effiong,
John Eme Eseme
Issue:
Volume 8, Issue 6, November 2019
Pages:
276-286
Received:
13 October 2019
Accepted:
12 November 2019
Published:
4 December 2019
Abstract: In this work, volatility of Internally Generated Revenue of Akwa Ibom State with the contributory effects of its components was the major interest. Autoregressive Conditional Heteroscedasticity ARCH (1) model adopted revealed volatility in the IGR. This motivated investigation of the components as contributory factors to the volatility. The OLS regression of IGR volatility on the K-components revealed the contribution of each component to the IGR volatility. The F test result showed overall fitness of the regression model. Individual T test placed tax revenue volatility higher than any other component. The volatility in the tax revenue is explained by the inconsistency in the growing trend of the tax revenue. This is attributed to laxities in the revenue generation mechanism, therefore posing challenges to the revenue system. The revenue generation system in the state requires sound leadership in the Board of Internal Revenue, good revenue driven policy, transparent tax revenue consulting and innovative approaches by the labour force for improved revenue system. Government willingness to address the prevailing issues would enhance stability in the revenue generation, therefore, helping to reduce volatility and cope with the challenges of financial planning in Akwa Ibom State.
Abstract: In this work, volatility of Internally Generated Revenue of Akwa Ibom State with the contributory effects of its components was the major interest. Autoregressive Conditional Heteroscedasticity ARCH (1) model adopted revealed volatility in the IGR. This motivated investigation of the components as contributory factors to the volatility. The OLS reg...
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Posterior Predictive Checks for the Generalized Pareto Distribution Based on a Dirichlet Process Prior
Wilson Moseki Thupeng,
Boikanyo Mokgweetsi,
Thuto Mothupi
Issue:
Volume 8, Issue 6, November 2019
Pages:
287-295
Received:
14 October 2019
Accepted:
4 December 2019
Published:
25 December 2019
Abstract: Extreme value modelling is widely applied in situations where accurate assessment of the behavior of a process at high levels is needed. The inherent scarcity of extreme value data, the natural objective of predicting future extreme values of a process associated with modelling of extremes and the regularity assumptions required by the likelihood and probability weighted moments methods of parameter estimation within the frequentist framework, make it imperative for a practitioner to consider Bayesian methodology when modelling extremes. Within the Bayesian paradigm, the widely used tool for assessing the fitness of a model is by using posterior predictive checks (PPCs). The method involves comparing the posterior predictive distribution of future observations to the historical data. Posterior predictive inference involves the prediction of unobserved variables in light of observed data.. This paper considers posterior predictive checks for assessing model fitness for the generalized Pareto model based on a Dirichlet process prior. The posterior predictive distribution for the Dirichlet process based model is derived. Threshold selection is done by minimizing the negative differential entropy of the Dirichlet distribution. Predictions are drawn from the Bayesian posterior distribution by Markov chain Monte Carlo simulation (Metropolis-Hastings Algorithm). Two graphical measures of discrepancy between the predicted observations and the observed values commonly applied in practical extreme value modelling are considered, the cumulative distribution function and quantile plots. To support these, the Nash-Sutcliffe coefficient of model efficiency, a numerical measure that evaluates the error in the predicted observations relative to the natural variation in the observed values is used. Finite sample performance of the proposed procedure is illustrated through simulated data. The results of the study suggest that posterior predictive checks are reasonable diagnostic tools for assessing the fit of the generalized Pareto distribution. In addition, the posterior predictive quantile plot seems to be more informative than the probability plot. Most interestingly, selecting the threshold by minimizing the negative differential entropy of a Dirichlet process has the added advantage of allowing the analyst to estimate the concentration parameter from the model, rather than specifying it as a measure of his/her belief in the proposed model as a prior guess for the unknown distribution that generated the observations. Lastly, the results of application to real life data show that the distribution of the annual maximal inflows into the Okavango River at Mohembo, Botswana, can be adequately described by the generalized Pareto distribution.
Abstract: Extreme value modelling is widely applied in situations where accurate assessment of the behavior of a process at high levels is needed. The inherent scarcity of extreme value data, the natural objective of predicting future extreme values of a process associated with modelling of extremes and the regularity assumptions required by the likelihood a...
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Kriging and Simulation in Gaussian Random Fields Applied to Soil Property Interpolation
Issue:
Volume 8, Issue 6, November 2019
Pages:
296-305
Received:
28 March 2019
Accepted:
24 October 2019
Published:
30 December 2019
Abstract: Spatial modeling is increasingly prominent in many fields of science as statisticians attempt to characterize variability of the processes that are spatially indexed. This paper shows that the Gaussian random field framework is useful for characterizing spatial statistics for soil properties. A sample of soil properties in 94 spatial locations are taken from a field (186.35m×211.44m) wide in northern Ethiopia, Karsa-Malima. We use observations of organic carbon (OC) from the site in our study. Box-Cox transformation is used because of OC follows non-Gaussian distributions. We develop ordinary kriging which is universal kriging with unknown trend models which enables us to predict any point within the field even outside the field up to the “Range” of the model. In this thesis work we predict 100×100 grids (10000 points) using kriging interpolation models. More over in each of these 10000 locations 1000 conditional simulations are made. Interestingly prediction using universal kriging and mean of conditional simulations agree in expectation and kriging variance. For covariance and/or variogram modeling and for parameter estimation we used least square principle and maximum likelihood estimation method. The classical geostatistical approach known as kriging is used as a spatial model for spatial prediction with associated spatial variances. Moreover, conditional simulation is performed. From ordinary kriging model results, predictions are accurate when predictions are close to observation locations. Prediction variance in the observed locations is close to the nugget effect.
Abstract: Spatial modeling is increasingly prominent in many fields of science as statisticians attempt to characterize variability of the processes that are spatially indexed. This paper shows that the Gaussian random field framework is useful for characterizing spatial statistics for soil properties. A sample of soil properties in 94 spatial locations are ...
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