-
Regression Approach to Parameter Estimation of an Exponential Software Reliability Model
Albert Orwa Akuno,
Timothy Mutunga Ndonye,
Janiffer Mwende Nthiwa,
Luke Akong’o Orawo
Issue:
Volume 5, Issue 3, May 2016
Pages:
80-86
Received:
10 March 2016
Accepted:
5 April 2016
Published:
21 April 2016
Abstract: Mathematical studies about the likelihood of failures of software systems have been advanced by various researchers. These studies have modeled the behavior of software systems by using failure times and time between failures in the past. The Goel-Okumoto software reliability model is amongst the many software reliability models proposed to model the failure behavior of software systems. To be able to use the model in software reliability assessment, it is important to estimate its parameters α and β and the intensity function λ(t). In this paper, classical parametric regression methods have been utilized in the estimation of the parameters α and β, the intensity function and the mean time between failures of the Goel-Okumoto software reliability model. The parameters α and β and the mean time between failures (MTBF) of the Goel-Okumoto software model have been estimated using the maximum likelihood estimation (MLE) method, regression approach applied to the model and simple linear regression model without assuming the Goel-Okumoto model. When these three estimation methods were validated using root mean squared error (RMSE) and mean absolute value difference (MAVD), which are the common error measurement criteria, regression approach applied to the Goel-Okumoto model outperformed MLE and simple linear regression estimation methods.
Abstract: Mathematical studies about the likelihood of failures of software systems have been advanced by various researchers. These studies have modeled the behavior of software systems by using failure times and time between failures in the past. The Goel-Okumoto software reliability model is amongst the many software reliability models proposed to model t...
Show More
-
Dependency of the Distribution of Salmonella-Specific Antibodies SP-Ratios on Weight and Sampling Time
Isaac Akpor Adjei,
Md. Rezaul Karim,
Rachid Muleia,
Peter Jouck
Issue:
Volume 5, Issue 3, May 2016
Pages:
87-93
Received:
28 March 2016
Accepted:
14 April 2016
Published:
26 April 2016
Abstract: Salmonella is one of the major sources of toxin-infection in humans worldwide and is due to transmission of pathogens via pork. This paper aims at investigating the effect of season and animal weight on SP-ratio. Pigs were sampled from different herds and SP-ratios were measured and categorized into two different groups. Depending on the categorization of the response and whether or not clustering is taken into account, different binary logistic and multicategory logit models were considered. Without taking clustering into account, ordinary logistic regression, adjacent logit, continuation-ratio logit and proportional odds model were fitted. GEE and GLMM were considered to correct for the herd-effect. Among the multicategory logit models, the proportional odds model is preferred, since it did not reject the assumption of common slopes. However, regarding the goodness-of-fit test, this model did not adequately fit the data. Both GEE and GLMM have their advantages, depending on the specific focus and question of interest. In all models, the interaction between weight and season was not significant. Weight was found significant, while season was insignificant in all models. As it was expected, weight as indicator for age was found to have a significant effect on SP-ratios.
Abstract: Salmonella is one of the major sources of toxin-infection in humans worldwide and is due to transmission of pathogens via pork. This paper aims at investigating the effect of season and animal weight on SP-ratio. Pigs were sampled from different herds and SP-ratios were measured and categorized into two different groups. Depending on the categoriza...
Show More
-
A Multivariate Statistical Research on Engagement of University Students: A Case Study in Greece
Issue:
Volume 5, Issue 3, May 2016
Pages:
94-100
Received:
7 April 2016
Accepted:
18 April 2016
Published:
28 April 2016
Abstract: In the present article we study the engagement of University students. Data drawn from the Faculty of Health and Caring Professions of a Greek University, are properly analyzed via inferential statistics in order to detect characteristics that affect significantly the engagement of students. Factor analysis has been also applied and revealed the expected structure of the measurement scale that has been used. Moreover, cluster analysis based on total score contributed to the identification of the crucial role of several demographics.
Abstract: In the present article we study the engagement of University students. Data drawn from the Faculty of Health and Caring Professions of a Greek University, are properly analyzed via inferential statistics in order to detect characteristics that affect significantly the engagement of students. Factor analysis has been also applied and revealed the ex...
Show More
-
Modeling and Forecasting Consumer Price Index (Case of Rwanda)
Habimana Norbert,
Anthony Wanjoya,
Anthony Waititu
Issue:
Volume 5, Issue 3, May 2016
Pages:
101-107
Received:
10 April 2016
Accepted:
20 April 2016
Published:
3 May 2016
Abstract: Consumer price index is a measure of the average change over time in the price of consumer items, goods and services that households buy for day to day living. It is one of the main indicators of economic performance and also the key indicator of the results of the monetary policy of the country, because of its wide use as a measure of inflation. The main objective of this research was to model the dynamic of CPI and to forecast its future values in the short term. Therefore, to come up with a model and forecasts of CPI, Box and Jenkins methodology were used which consists of three main steps; Model Identification, Parameter Estimation and Diagnostic Checking. Therefore, ARIMA (4,1,6) was selected as a potential model which can fits well data, as well as to make also accurate forecast. Hence, the forecast was made for 12 months ahead of the year 2016, and the findings have shown that the CPI was likely to continue rising up with time.
Abstract: Consumer price index is a measure of the average change over time in the price of consumer items, goods and services that households buy for day to day living. It is one of the main indicators of economic performance and also the key indicator of the results of the monetary policy of the country, because of its wide use as a measure of inflation. T...
Show More
-
A Multivariate Analysis of the Effect of Mobile Phone Money Transfer on Micro and Small Enterprises, Thika Town (Kenya)
Beatrice Karanja Kimani,
Jemimah Wangui Muraya,
Christopher Ouma Onyango
Issue:
Volume 5, Issue 3, May 2016
Pages:
108-114
Received:
13 April 2016
Accepted:
20 April 2016
Published:
3 May 2016
Abstract: The introduction of mobile money transfers (MMT) services has increased access to banking services among business entrepreneurs. This facilitates quick and secure platform for small savings to a majority of both rural and urban populations. The MSEs are increasingly adopting the use of mobile money transfers to increase the quality of their services and promote growth. However, limited research has been done on the impact of MMT services on the small and micro-enterprises. This study aimed at investigating the effect of mobile money transfers on the MSEs success factors, growth and expansion. The survey was conducted through administration of questionnaires and interviews of MSEs operators in Thika Town, Kenya. Data analysis was done using multivariate techniques, to a deeper extent the factor analysis. It was evident from the factor analysis, using principal component analysis that three factors were extracted which loaded highly on given variables. The factors were suggested to be demographic, accessibility and satisfaction, after considering the variables that loaded on each factor. The findings were expected to be useful to the mobile payments technology providers, by offering greater entrepreneur support to the micro business operators and enhance customers’ convenience to use the technology. The government can also use these findings when designing appropriate plan of action to encourage many more business operators to adopt the MMT services through funding and other platforms.
Abstract: The introduction of mobile money transfers (MMT) services has increased access to banking services among business entrepreneurs. This facilitates quick and secure platform for small savings to a majority of both rural and urban populations. The MSEs are increasingly adopting the use of mobile money transfers to increase the quality of their service...
Show More
-
Performance of Two Generating Mechanisms in Detection of Outliers in Multivariate Time Series
Olufolabo Olusesan Oluyomi.,
Shittu Olarenwaju Ismail.,
Adepoju Kazeem Adesola.
Issue:
Volume 5, Issue 3, May 2016
Pages:
115-122
Received:
5 April 2016
Accepted:
25 April 2016
Published:
10 May 2016
Abstract: This work is focused on developing two outlier generating mechanisms for the detection of outliers in the multivariate time series setting that is capable of ameliorating the swamping effect on regular observations in time series data. Specifying two-variable Vector Autoregressive (VAR) models and assuming innovative and multiplicative effect of outliers on time series data, the magnitude and variance of outlier were derived for the generating models by method of least squares. A modified test statistics were also developed to detect single outliers both in the response and explanatory variables. Real and simulated data were used to establish the validity of the models. The results show that the multiplicative is better than the additive model in terms of the number of outliers detected and the residual variance. This result is in line with previous studies in outlier detection in univariate time series.
Abstract: This work is focused on developing two outlier generating mechanisms for the detection of outliers in the multivariate time series setting that is capable of ameliorating the swamping effect on regular observations in time series data. Specifying two-variable Vector Autoregressive (VAR) models and assuming innovative and multiplicative effect of ou...
Show More
-
Actuarial Analysis of Single Life Status and Multiple Life Statuses
Abonongo John,
Luguterah Albert
Issue:
Volume 5, Issue 3, May 2016
Pages:
123-131
Received:
12 April 2016
Accepted:
22 April 2016
Published:
10 May 2016
Abstract: Actuaries frequently employ probability models to analyse situations involving uncertainty. They are also not simply interested in modelling the future states of a subject but also model cash flows associated with future states. This study compared single life status and multiple life statuses using life functions. The expected time until death, annuity payments, insurance payable and premiums were estimated using age as a risk factor. The analysis also employed the De Moirve’s law on mortality in estimating the rate of mortality. The analysis revealed that, the expected time until death for single life status and multiple life statuses are all increasing functions of age. It was realized also that, the premium for single life status was increasing with age and the same with multiple life statuses. But the premium for single life was higher than multiple life statuses. In the case of the multiple life statuses, it was revealed that, premium for joint life was higher than the last survivor and that a change in the interest rate or force of interest and the benefit did not changed the trend in premium payments.
Abstract: Actuaries frequently employ probability models to analyse situations involving uncertainty. They are also not simply interested in modelling the future states of a subject but also model cash flows associated with future states. This study compared single life status and multiple life statuses using life functions. The expected time until death, an...
Show More
-
Human Fertility Behavior Through Birth Interval Models: Overview
Issue:
Volume 5, Issue 3, May 2016
Pages:
132-137
Received:
18 March 2016
Accepted:
24 March 2016
Published:
17 May 2016
Abstract: Fertility is one of the responsible factors for the growth of human population. The demographers have given priority to understanding of the determinants of fertility through statistical techniques. Analytical models are suitable and appropriate tools and are widely used for better understanding of the phenomenon of the human fertility behavior. In other words, these models are useful in describing the action and interaction among various factors as well as for predicting the change in fertility behavior. The analytic models play an important role in estimation and interpretation of the fertility behaviors. In this paper, discuss the of birth intervals model based on realistic assumptions of human reproductive process, indirectly incorporating socio-cultural, bio-demographic factors, taboos and also use of contraceptive practices. In these derived models to describe the variation in the length of closed, forward, straddling and open birth interval with the realistic assumption that all the females are not exposed to the risk of conception immediately after the termination of post-partum amenorrhea (PPA) due to some factors or contraceptive practices. In these models, fecundability (λ) has been considered to be constant over the study period. The duration of time from the point of termination of PPA to the state of exposure has been taken as random variable which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameter (λ) through different derived models.
Abstract: Fertility is one of the responsible factors for the growth of human population. The demographers have given priority to understanding of the determinants of fertility through statistical techniques. Analytical models are suitable and appropriate tools and are widely used for better understanding of the phenomenon of the human fertility behavior. In...
Show More
-
An Almost Unbiased Estimator in Group Testing with Errors in Inspection
Langat Erick Kipyegon,
Tonui Benard Cheruiyot,
Langat Reuben Cheruiyot
Issue:
Volume 5, Issue 3, May 2016
Pages:
138-145
Received:
26 April 2016
Accepted:
9 May 2016
Published:
25 May 2016
Abstract: The idea of pooling samples into pools as a cost effective method of screening individuals for the presence of a disease in a large population is discussed. Group testing was designed to reduce diagnostic cost. Testing population in pools also lower misclassification errors in low prevalence population. In this study we violate the assumption of homogeneity and perfect tests by investigating estimation problem in the presence of test errors. This is accomplished through Maximum Likelihood Estimation (MLE). The purpose of this study is to determine an analytical procedure for bias reduction in estimating population prevalence using group testing procedure in presence of tests errors. Specifically, we construct an almost unbiased estimator in pool-testing strategy in presence of test errors and compute the modified MLE of the prevalence of the population. For single stage procedures, with equal group sizes, we also propose a numerical method for bias correction which produces an almost unbiased estimator with errors. The existence of bias has been shown with the help of Taylor's expansion series, for group sizes greater than one. The indicator function with errors is used in the development of the model. A modified formula for bias correction has been analytically shown to reduce the bias of a group testing model. Also, the Fisher information and asymptotic variance has been shown to exist. We use MATLAB software for simulation and verification of the model. Then various tables are drawn to illustrate how the modified bias formula behaves for different values of sensitivities and specificities.
Abstract: The idea of pooling samples into pools as a cost effective method of screening individuals for the presence of a disease in a large population is discussed. Group testing was designed to reduce diagnostic cost. Testing population in pools also lower misclassification errors in low prevalence population. In this study we violate the assumption of ho...
Show More
-
On Consistency of Tests for Stationarity in Autoregressive and Moving Average Models of Different Orders
Akeyede Imam,
Danjuma Habiba,
Bature Tajudeen Atanda
Issue:
Volume 5, Issue 3, May 2016
Pages:
146-153
Received:
26 April 2016
Accepted:
11 May 2016
Published:
25 May 2016
Abstract: The most important assumptions about econometrics and time series data is stationarity, This study therefore suggests that, in trying to decide by classical methods whether economic data are stationary or not, it would be useful to perform tests of the null hypothesis of stationarity as well as tests of the null hypothesis of a unit root. The study compared power and type I error of Augmented Dickey-Fuller (ADF), Kwiatkowski, Phillips, Schmidt and Shin (KPSS) and Phillips and Perron (PP) to test the null hypothesis of stationarity against the alternative of a unit root at different order of autoregressive and moving average and various sample sizes. Simulation studies were conducted using R statistical package to investigate the performance of the tests of stationarity and unit root at sample size 20, 40, ..., 200 at first, second and third orders of autoregressive (AR), moving average (MA) and mixed autoregressive and moving average (ARMA) models. The relative performance of the tests was examined by their percentage of their powers and type I errors. The study concluded that PP is the best over all the conditions considered for the models, sample sizes and orders. However, in terms of type 1 error rate PP still is the best.
Abstract: The most important assumptions about econometrics and time series data is stationarity, This study therefore suggests that, in trying to decide by classical methods whether economic data are stationary or not, it would be useful to perform tests of the null hypothesis of stationarity as well as tests of the null hypothesis of a unit root. The study...
Show More
-
Parameter Estimation of Kumaraswamy Distribution Based on Progressive Type II Censoring Scheme Using Expectation-Maximization Algorithm
Wafula Mike Erick,
Kemei Anderson Kimutai,
Edward Gachangi Njenga
Issue:
Volume 5, Issue 3, May 2016
Pages:
154-161
Received:
3 May 2016
Accepted:
23 May 2016
Published:
1 June 2016
Abstract: This project considers the parameter estimation problem of test units from Kumaraswamy distribution based on progressive Type-II censoring scheme. The progressive Type-II censoring scheme allows removal of units at intermediate stages of the test other than the terminal point. The Maximum Likelihood Estimates (MLEs) of the parameters are derived using Expectation-Maximization (EM) algorithm. Also the expected Fisher information matrix based on the missing value principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. Through simulations, the behaviour of these estimates are studied and compared under different censoring schemes and parameter values. It’s concluded that for an increasing sample; the estimated parameter values become closer to the true values, the variances and widths of the confidence intervals reduce. Also, more efficient estimates are obtained with censoring schemes concerned with removals of units from their right.
Abstract: This project considers the parameter estimation problem of test units from Kumaraswamy distribution based on progressive Type-II censoring scheme. The progressive Type-II censoring scheme allows removal of units at intermediate stages of the test other than the terminal point. The Maximum Likelihood Estimates (MLEs) of the parameters are derived us...
Show More
