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Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique
Otieno Okumu Kevin,
John Matuya,
Muthiga Nganga
Issue:
Volume 10, Issue 6, November 2021
Pages:
226-232
Received:
10 March 2021
Accepted:
22 March 2021
Published:
10 November 2021
Abstract: From the past studies, we realized that minimum distance estimation technique is not commonly used for fitting wind speed data to a distribution yet it is believed to the best alternative for Maximum Likelihood Estimation (MLE) method which is known to give good estimates than Least Square Estimates (LSE) and Method of Moments (MOM). To achieve this, the study aims at fitting data to a probability distribution using minimum distance estimation techniques to find the best distribution. The study uses wind speed data from five sites in Narok county namely; Irbaan primary, Imortott primary, Mara conservancy, Oldrkesi and Maasai Mara University. The best wind speed models were examined using the Cullen and Frey graph and a suitability test on the models done using Kolmogorov-Smirnov statistical test of goodness of fit. The wind speed data are fitted to the recommended distributions using minimum distance estimation techniques. The best distribution was identified using Akaike's Information Criterion (AIC) and Bayesian Information criterion (BIC). From the distribution comparison for the two and three parameter distributions, gamma is the best in all cases. Gamma with three parameter distribution gives lower AIC and BIC values and model comparison test showing that gamma 3-parameter is the better than gamma with 2-parameters. The study concluded that gamma distribution with three parameters is the best distribution for fitting wind speed data with the three parameters given as; threshold parameter of 0.1174, shape parameter of 1.8646 and scale parameter of 0.9937.
Abstract: From the past studies, we realized that minimum distance estimation technique is not commonly used for fitting wind speed data to a distribution yet it is believed to the best alternative for Maximum Likelihood Estimation (MLE) method which is known to give good estimates than Least Square Estimates (LSE) and Method of Moments (MOM). To achieve thi...
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Modeling of Survival of HIV Patients by Stages of Immune Suppression and Opportunisic Infections
Edidiong Michael Udofia,
Edith Uzoma Umeh,
Chrisogonus Kelechi Onyekwere
Issue:
Volume 10, Issue 6, November 2021
Pages:
233-242
Received:
21 July 2021
Accepted:
4 August 2021
Published:
12 November 2021
Abstract: Globally, there are many people living with Human Immune Deficiency Virus (HIV), and the rate increases every day. Research has shown that Nigeria is the second largest country with HIV epidemic, as many are living with advanced HIV. People with advanced stage of HIV infection are vulnerable to secondary infections and malignancies, generally termed Opportunistic Infections (OIs). This is because, these infections take advantage of the opportunity offered by a weakened immune system, thereby causing complications in HIV infected persons and causing harm to individuals. The aim of this work is to investigate and model the survival, by stages of immune suppression and opportunistic infections on patients undergoing Antiretroviral Therapy (ART), in a population in South-South Nigeria. 221 Human Immune Deficiency Virus (HIV) patients data obtained from St. Luke’s Hospital, Anua, for the period of 2008 to 2017 were used. Four different parametric models, the extreme, lognormal, logistics, log-logistics distributions and nonparametric Kaplan-Meier method were considered in order to carry out modeling of survival, and survival of patients respectively. The models were subjected to life application using lifetime datasets and a test of goodness of fit was made using Akaike’s Information Criteria (AIC) and Bayesian Information Criteria (BIC) criteria. From the results obtained, extremedistribution had the lowest AIC and BIC value, indicating that it is the best parametric model for modeling survival of HIV patients in the hospital. Also, the Kaplan-Meier method indicates that the survival experience of female patients were favorable than male patients.
Abstract: Globally, there are many people living with Human Immune Deficiency Virus (HIV), and the rate increases every day. Research has shown that Nigeria is the second largest country with HIV epidemic, as many are living with advanced HIV. People with advanced stage of HIV infection are vulnerable to secondary infections and malignancies, generally terme...
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On the Performance of a Class of Generalized Linear Mixed Model on Some Psychiatric Patients' Data
Omobolaji Yusuf Halid,
Samuel Oluwaseun Adejuwon,
Vincent Gbenga Jemilohun
Issue:
Volume 10, Issue 6, November 2021
Pages:
243-248
Received:
13 September 2021
Accepted:
5 October 2021
Published:
27 November 2021
Abstract: A generalized linear mixed model (GLMM) is an extension to the generalized linear mixed (GLM) in which the linear predictor contains random effects in addition to the usual fixed effects. They also inherit from GLMs the idea of extending linear mixed models to non-normal data. There are several applications of various types of generalized linear mixed models (GLMMs) to various fields, especially in the areas of health and biological sciences. In this our study Poisson logistic mixed regression model (a class of GLMM) was adopted to investigate the performance of the above mentioned method on some psychiatric patients’ data. A clinical trial of ninety (90) mentally disordered patients was examined in this work. Patients suffering from some level of psychiatric disorder were randomized to receive either Amitryphylline or Benzhexol in addition to other therapy. This work is motivated by Thall and Vail, which investigated the performance of the Poisson logistic mixed model on some epileptics’ data. The two types of therapy have little effect on the patients, but the interaction (between treatments and visits) has a substantial impact on the patients. The number of seizures is reduced by visits, and a combination of visits and medicines decreases the number of seizures. The fact that the treatments are insignificant suggests that mental disorders are mostly treatable with currently available medications. These drugs only ‘manage' them for a short period of time.
Abstract: A generalized linear mixed model (GLMM) is an extension to the generalized linear mixed (GLM) in which the linear predictor contains random effects in addition to the usual fixed effects. They also inherit from GLMs the idea of extending linear mixed models to non-normal data. There are several applications of various types of generalized linear mi...
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Diagnostic Analysis of Weather Variables for Forecasting Rainfall Patterns in Kenya Using Bayesian Vector Autoregressive Model
Gitonga Harun Mwangi,
Joseph Koske,
Mathew Kosgei
Issue:
Volume 10, Issue 6, November 2021
Pages:
249-256
Received:
15 October 2021
Accepted:
5 November 2021
Published:
9 December 2021
Abstract: Time series has fundamental importance in various practical domains in the world, more so in modeling and forecasting. Many important models have been proposed to improve the accuracy of their prediction. Global warming has been a big challenge to the world in affecting economic and Agricultural activities. It causes drastic weather changes, which are characterized by precipitation and temperature. Rainfall prediction is one of the most important and challenging tasks in today’s world. The objective of this study was to conducted a diagnostic analyzes of weather variables which were used to model the rainfall patterns by use of Bayesian Vector Autoregressive (BVAR). The diagnostic analyzes was done after the normalization of the data. The data was found to be stable after first differencing and it was tested using Augmented Dicker Fuller (ADF) and Phillips-Perron (PP) test. The tests were found to have the P-values that were statistically significant. The Granger Causality test was also conducted and found to be statistically significant. The Ljung-Box test of residuals, shows that the graphs of these residuals produced, appeared to explain all the available information in the forecasted model. The mean of the residuals was near to zero and therefore no significant correlation was witnessed. The time plot shows that the variation of the residuals remains much the same across the historical data, apart from the two values that were beyond 0.2 or -0.2 in Zone Two, and therefore the residual variance was treated as constant. The histogram shows that the residuals were normally distributed, which represented gaussian behavior. The ACF graph, shows that the spikes were within the required limits, so the conclusion was that the residuals had no autocorrelation of the residuals. The Ljung-Box test shows that the developed model was good for forecasting. Finally, the researcher recommends application of other techniques like Random Forest and Bootstrapping technique to check whether the accuracy may further be improved from other models.
Abstract: Time series has fundamental importance in various practical domains in the world, more so in modeling and forecasting. Many important models have been proposed to improve the accuracy of their prediction. Global warming has been a big challenge to the world in affecting economic and Agricultural activities. It causes drastic weather changes, which ...
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On Approximation of Copulas, Solution of Elliptic Problem, Using the Finite Difference Method: Generalization
Remi Guillaume Bagré,
Frédéric Béré,
Kpèbbèwèrè Cédric Somé,
Paliguiwindé Dieudonné Ibrango
Issue:
Volume 10, Issue 6, November 2021
Pages:
257-261
Received:
26 October 2021
Accepted:
26 November 2021
Published:
9 December 2021
Abstract: In this paper, we generalize a copula construction method discussed in one of our papers. For this purpose we consider the general form of a linear elliptic PDE. Indeed, a physical interpretation of elliptic equations comes from the notion of conservative flow given by a gradient. This notion provides a mathematical model for equilibrium conservation laws in linear behaviour. This can be applied to many areas of science. Thus, the aim of this paper is to construct a new class of bivariate copulas by solving an elliptic partial differential equation with a Dirichlet condition at the boundary. Copulas belonging to this class allow us to study the stochastic behaviour of the notion of conservative flows. In other words, these copulas will allow us to have an idea on the dependence of those physical phenomena which are governed by elliptic PDEs. For this purpose, we use a discretization method which is the finite difference method which is a common technique for finding approximate solutions of partial differential equations that consists in solving a system of relations (numerical scheme) connecting the values of the unknown functions at some points sufficiently close to each other. For the finite difference method, a mesh is made. This is a set of isolated points called nodes located in the domain of definition of the functions subject to the partial differential equations, a grid on which only the nodes of which the unknowns corresponding to the approximate values of these functions are defined. The mesh also includes nodes located on the boundary of the domain (or at least "close" to this boundary) in order to be able to impose the boundary conditions and/or the initial condition with sufficient accuracy. The primary quality of a mesh is to cover the domain in which it develops as well as possible, to limit the distance between each node and its nearest neighbour. However, the mesh must also allow the discrete formulation of the differentiation operators to be expressed: for this reason, the nodes of the mesh are most often located on a grid whose main directions are the axes of the variables. In the main results of this paper (see section 3), we give a discretization of the solution of the problem followed by a simulation with the MATLAB software of this approximated solution and presenting the discretization errors.
Abstract: In this paper, we generalize a copula construction method discussed in one of our papers. For this purpose we consider the general form of a linear elliptic PDE. Indeed, a physical interpretation of elliptic equations comes from the notion of conservative flow given by a gradient. This notion provides a mathematical model for equilibrium conservati...
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