-
Estimation of Parameters of the Two-Parameter Rayleigh Distribution Based on Progressive Type-II Censoring Using Maximum Likelihood Method via the NR and the EM Algorithms
Murithi Daniel Fundi,
Edward Gachangi Njenga,
Kemboi George Keitany
Issue:
Volume 6, Issue 1, January 2017
Pages:
1-9
Received:
15 November 2016
Accepted:
30 November 2016
Published:
20 December 2016
Abstract: In this article, Maximum likelihood estimates for the shape and scale parameters of two-parameter Rayleigh distribution are obtained based on progressive type-II censored samples using the Newton-Raphson (NR) method and the Expectation-Maximization (EM) algorithm. A simple algorithm discussed in [2-3] is used for generating progressive type-II censored samples. Based on this censoring scheme, approximate asymptotic variances are derived and used to construct approximate confidence intervals of the parameters. The performance of these two maximum likelihood estimation algorithms is compared in terms of simulation results of root mean squared error (RMSE) and the coverage rates. Simulation results showed that in nearly all the combination of simulation conditions the estimators based on the EM algorithm have less root mean squared error (RMSE) and narrower widths of confidence intervals compared to those obtained using the NR algorithm. Finally, an illustrative example with real-life data sets is provided to illustrate how maximum likelihood estimation using the two algorithms works in practice.
Abstract: In this article, Maximum likelihood estimates for the shape and scale parameters of two-parameter Rayleigh distribution are obtained based on progressive type-II censored samples using the Newton-Raphson (NR) method and the Expectation-Maximization (EM) algorithm. A simple algorithm discussed in [2-3] is used for generating progressive type-II cens...
Show More
-
Modeling Maternal Risk Factors Affecting Low Birth Weight Among Infants in Kenya
Nancy Wairimu Gathimba,
Anthony Wanjoya,
George Kipruto Kiplagat,
Levi Mbugua,
Koima Kibiwott
Issue:
Volume 6, Issue 1, January 2017
Pages:
22-31
Received:
8 December 2016
Accepted:
20 December 2016
Published:
18 January 2017
Abstract: The strong association of birth weight with infant mortality is the main focus of birth weight research, with the assumption that birth weight is a major determinant of infant survival. Studies on factors of low birth weight in Kenya have neglected the flexible approach of using smooth functions for some covariates in models. Such flexible approach reveals detailed relationship of covariates with the response. The study sought to investigate risk factors of low birth weight in Kenya by assuming a flexible approach for continuous covariates and geographical random effect. The study used semi parametric models to flexibly model the effects of selected covariates and spatial effects. Our spatial analysis is based on a flexible geo-additive model using the provinces as the geographic unit of analysis, which allows to separate smooth structured spatial effects from random effect. A Gaussian model for birth weight in grams and a binary logistic model for the binary outcome were fitted. Continuous covariates was modeled by the penalized (p) splines and spatial effects was smoothed by the two dimensional p-spline. The specific objectives of the study was to investigate factors of low birth weight in Kenya by taking into account the hierarchical nature of child birth weight factors using a Bayesian hierarchical model. The study used secondary data from Kenya 2014 demographic and health survey (KDHS) data. The study found that child birth order, mother weight and height are significant predictors of birth weight. Secondary education for mother, birth order categories 2-3 and 4-5, wealth index of richer family and mother height were significant predictors of child size at birth. The area associated with low birth weight was North Eastern and areas with increased risk to less than average size at birth were Central and Eastern. The study found support for the flexible modeling of some covariates that clearly have nonlinear influences. Nevertheless there was no strong support for inclusion of geographical spatial analysis. The spatial patterns and the maps generated could be used for targeting development efforts at a glance. These findings have important implications for targeting policy as well as the search for left-out variables that might account for these residual spatial patterns.
Abstract: The strong association of birth weight with infant mortality is the main focus of birth weight research, with the assumption that birth weight is a major determinant of infant survival. Studies on factors of low birth weight in Kenya have neglected the flexible approach of using smooth functions for some covariates in models. Such flexible approach...
Show More
-
A Model for Age-Specific Fertility Rate Pattern of India Using Skew-Logistic Distribution Function
Ruchi Mishra,
Kaushalendra Kumar Singh,
Anjali Singh
Issue:
Volume 6, Issue 1, January 2017
Pages:
32-37
Received:
26 December 2016
Accepted:
6 January 2017
Published:
3 February 2017
Abstract: Fertility governs central and positive role in the study of human population dynamics. The age-specific fertility pattern has a distinct shape for all human population, to describe which, a number of parametric models have been proposed. The purpose of this study is to develop a mathematical model for fitting age-specific fertility rate pattern of various states of India. Skew-logistic probability density function is used for building the model. The real data, to which this model has been fitted, is obtained from National Family Health Survey- III (2005-2006). The used model is very flexible in nature and hence is useful for modeling diverse fertility patterns which are observed across different states of India. The parameters of the model have been estimated through the method of non-linear least square. By fitting the model it is observed that the proposed model fits well on the fertility pattern for almost each state of the country.
Abstract: Fertility governs central and positive role in the study of human population dynamics. The age-specific fertility pattern has a distinct shape for all human population, to describe which, a number of parametric models have been proposed. The purpose of this study is to develop a mathematical model for fitting age-specific fertility rate pattern of ...
Show More
-
Principal Component Analysis of Crime Data in Gwagwalada Area Command, Abuja from 1995 – 2015
Nasiru Mukaila Olakorede,
Samuel Olorunfemi Adams,
Samuel Olayemi Olanrewaju
Issue:
Volume 6, Issue 1, January 2017
Pages:
38-43
Received:
15 July 2016
Accepted:
25 July 2016
Published:
6 February 2017
Abstract: This paper analyses Abuja crime data which consists of the averages of twenty major crimes reported to the police for the period 1995 – 2015. Correlation analysis and principal component analysis (PCA) were employed to explain the correlation between the crimes and to determine the distribution of the crimes over the three Area Councils under the Gwagwalada Area Command. The result has shown a significant correlation between robbery and rape, grievous hurt and wound (GHW), theft, assault, murder and unlawful escape. Gwagwalada Area Council has the highest overall crime rate i.e. Rape, Robbery, GHW, Theft, Assault, Murder and unlawful escape in the Area Command. Unlawful possession, breach of peace and broken store are more prevalence in Kwali Area Council while Vehicle theft, car stealing and burglary are more prevalence in Kuje Area Council Area. The PCA has suggested retaining three components (Rape, Robbery and GHW) that explain about 86.873 percent of the total variability of the data set.
Abstract: This paper analyses Abuja crime data which consists of the averages of twenty major crimes reported to the police for the period 1995 – 2015. Correlation analysis and principal component analysis (PCA) were employed to explain the correlation between the crimes and to determine the distribution of the crimes over the three Area Councils under the G...
Show More
-
Multivariate Regression Analysis of Oil Price Volatility on GDP Growth in Kenya
Issue:
Volume 6, Issue 1, January 2017
Pages:
44-51
Received:
6 January 2017
Accepted:
16 January 2017
Published:
20 February 2017
Abstract: Despite Oil being one of the key drivers of the world economy, the recent fluctuations in oil prices has brought concerns about possible slowdowns in economic growth globally. To cushion their economies from these oil price volatility shocks, a number of developing countries have made structural reforms in their macroeconomic policies as far as domestic petroleum pricing system is concerned. In line with this, Kenya has undertaken to reform the energy sector so as to make it competitive, efficient as well as attracting investment in the sector. The main objective of this study was to investigate if volatility of oil price had an effect on Kenya’s GDP growth rate with Exchange rate and Inflation rate as intervening variables. The study used quarterly data from KNBS, CBK and ERC for the periods 2004 to 2013 to achieve its objective and all analysis were done in R. Analysis showed that fluctuation of Crude oil price in the international market coupled with fluctuations in the exchange rate and inflation rate determined 86.9 per cent of the trend in GDP growth rate. The study found that when crude oil price increases by KSh 1,000 per barrel, the Kenya shilling weakens by a single Kenya shilling for every US dollar and the inflation rate goes up by 1 per cent, then the GDP growth rate decreases by 0.132 percentage points (p=0.000). The study also found that the model used had no serial autocorrelation meaning that the error terms of the regression model at any given two different quarters were linearly uncorrelated. Moreover, Goldfeld-Quandt test statistic was found to be significantly higher than 5% or 1% significance levels. This was despite a plot graph of residuals vs the fitted values of GDP growth rate showing unequal distribution of residuals as the values of fitted GDP growth rate increased. Therefore the model was free from heteroscedasticity. The government should therefore focus on stabilizing exchange rate, increase domestic energy production to reduce reliance on importation of petroleum products and control the level of inflation.
Abstract: Despite Oil being one of the key drivers of the world economy, the recent fluctuations in oil prices has brought concerns about possible slowdowns in economic growth globally. To cushion their economies from these oil price volatility shocks, a number of developing countries have made structural reforms in their macroeconomic policies as far as dom...
Show More
-
Construction Procedure for Non-trivial T-designs
John Chibayi,
David Alila,
Fredrick Onyango
Issue:
Volume 6, Issue 1, January 2017
Pages:
52-60
Received:
20 July 2016
Accepted:
8 August 2016
Published:
22 February 2017
Abstract: A t-design is a generation of balanced incomplete block design (BIBD) where λ is not restricted to the blocks in which a pair of treatments occurs but to the number of blocks in which any t treatments (t = 2,3…) occurs. The problem of finding all parameters (t, v, k, λt) for which t-(v, k, λt) design exists is a long standing unsolved problem especially with λ=1 (Steiner System) as no Steiner t-designs are known for t ≥ 6 when v > k. The objective of this study therefore to develop new methods of constructing t-designs with t ≥ 3 and λ ≥1. In this study t-design is constructed by relating known BIB designs, combinatorial designs and algebraic structures with t-designs.
Abstract: A t-design is a generation of balanced incomplete block design (BIBD) where λ is not restricted to the blocks in which a pair of treatments occurs but to the number of blocks in which any t treatments (t = 2,3…) occurs. The problem of finding all parameters (t, v, k, λt) for which t-(v, k, λt) design exists is a long standing unsolved problem espec...
Show More
-
The Usage of Emergency Contraceptive Methods of Female Students in Hawassa University: A Case Study on Natural and Computational Science
Gezahegn Mekonnen,
Nebro Wendmagegn,
Demisew Gebiru
Issue:
Volume 6, Issue 1, January 2017
Pages:
61-71
Received:
17 December 2016
Accepted:
3 January 2017
Published:
24 February 2017
Abstract: Students in the higher education are found in adolescent period. Because of this, they are exposed to unwanted pregnancy that leads them to attempt illegal abortion, which results in death or illness or loss of future fertility and on the other hand, they are obliged to leave their education. The objective of the study is to assess the factors that affect female studentsemergency contraceptive usagein HU in case of Colleges of Natural and Computational Sciences. The significance of the study is to create some insight on the female students about contraceptive methods and to save female students from illegal abortion, unwanted pregnancy and other related problems. The source of data is primary data and it was collected using questionnaires. The statistical model under consideration was logistic regression and chi-square test of association. In descriptive part, the majority of student (77.6%) isless than 22 years old and42.4%are third year students. Sixty percent of the respondents come from urban area and the parental educational level of 36.8% of the respondents is higher education level. Most of the female students accessedinformation of emergency contraceptive from health professional, media and from their friends. 51.2% of Natural and Computational Sciences female students are familiar with ECM, but the rest 48.8% of female students not use emergency contraceptive at all. The usage of emergency contraceptive method are associated with where the female students heard and get the ECM, their marital status, parent’s educational level and batch of students. The female students usage of ECM affected by source and information about emergency contraceptive method (ECM), their marital status and batch of students. Hence HU should prepare panel discussion, post some poster which talk about ECM in some areas like in clinic, invite some guests from the family planning bureau to teach the students when and how to use the ECM.
Abstract: Students in the higher education are found in adolescent period. Because of this, they are exposed to unwanted pregnancy that leads them to attempt illegal abortion, which results in death or illness or loss of future fertility and on the other hand, they are obliged to leave their education. The objective of the study is to assess the factors that...
Show More
