by Abdallah S. A. Yaseen
Original Research
Interstitial cystitis (IC) is a chronic inflammatory condition that results in recurring discomfort or pain in the bladder and the surrounding pelvic region. In interstitial cystitis data base (ICDB) cohort study, the main target is to determine the influence of covariates, such as the demographic clinical characteristics of patients, on the longitudinal outcomes including the pain score (p), urinary urgency (u) and urinary frequency (f) which are three main indices reflecting IC symptoms. The ICDB data are mixed (discrete and continuous) longitudinal data. In longitudinal studies the continuous response may be non-normal, heavy tailed for example. The analysis of mixed longitudinal data is challenging due to several inherent features: (1) more than one outcome are followed for each subject over a period of time. (2) The longitudinal outcomes are subject to missingness that may be missing not at random (MNAR). This article proposes the analysis of mixed discrete and heavy tailed longitudinal outcomes subject to MNAR missingness using two different alternative algorithms. The continuous outcome is assumed to follow non-normal heavy tailed distribution. The proposed methodology is an extension of [1] and [2]. The proposed techniques are applied to Interstitial Cystitis data. Also, three simulation studies are conducted to validate the proposed techniques.
American Journal of Applied Mathematics and Statistics. 2022, 10(1), 28-38. DOI: 10.12691/ajams-10-1-5
Pub. Date: April 10, 2022
1728 Views4 Downloads
by K.A.D. Deshani, Liwan Liyanage-Hansen and Dilhari T. Attygalle
Original Research
With the advancement of technology, vast time related databases are created from a plethora of processes. Analyzing such data can be very useful, but due to the large volumes and their relevance to time, extracting useful information and implementing models can be very complex and time consuming. However, using a comprehensive exploratory study to extract hidden features of the data can mitigate this complexity to a great extent. The clustering approach is one such way to extract features but can be demanding with time related data, especially with a trend in the data series. This paper proposes an algorithm, based on regression tree approach, to cluster a time series with a trend, along with other relevant variables. The importance of this algorithm is avoiding the misleading cluster allocations that can be created through clustering a differenced time series. Initially it identifies a suitable consistent time window with no trend, and implements separate regression trees for each window, to obtain the clusters. Through exploring the clusters generated from these trees, a general cluster formation is identified suitable for all windows. This is illustrated using hourly electricity demand in Sri Lanka for five consecutive years. Six meaningful clusters were identified based on the day of the week, specialty, and the time of the day. These cluster memberships provide useful additional information on the data structure, independent of the trend component, and can be used as an additional feature for improving model accuracies.
American Journal of Applied Mathematics and Statistics. 2022, 10(1), 22-27. DOI: 10.12691/ajams-10-1-4
Pub. Date: March 23, 2022
1788 Views3 Downloads
by Arnold Kiura Njuki, Thomas Mageto and Anthony Ngunyi
Review Article
Biometric authentication system has become a mainstream solution across industries and devices. From securing highly confidential data to unlocking smartphones, biometrics have eliminated the hassle of remembering multiple complex passwords and PINs. It means that nobody can gain access to a device or system without your presence. This paper discusses a method which could be used in the testing process of biometric systems on the side of users and customers. Large –scale biometric systems traditionally undergo a series of tests beyond technology and scenario testing. These large-scale system tests are typically at the system level, not just the biometric subsystem level, and occur multiple times in the life of a system in such forms as factory acceptance tests before shipment, site or system acceptance tests before initiating operations, and in- use tests to ensure that performance remains at acceptable levels and/or to reset thresholds or other technical parameters. The conventional statistical methods use the binomial distribution to estimate the expected number of failure, but in the field of the biometrics the probability parameter can’t be constant which means that it is necessary to describe a process. The results have shown that the probability is characterized with two parameters of the beta distribution, and these are predictable from a smaller sample of the investigated population with the maximum likelihood method.
American Journal of Applied Mathematics and Statistics. 2022, 10(1), 14-21. DOI: 10.12691/ajams-10-1-3
Pub. Date: March 15, 2022
2371 Views6 Downloads
by Duromola M.K.
Original Research
The solution of Differential Equations is an important topic for deliberation among scientists. However, until today, nothing is known on a single-step block method of p-stable for solving third-order Differential Equations (IVPs) whose accuracy is ninth order. This paper focuses on the derivation, analysis, and implementation of the one-step implicit hybrid block method with seven off-step points for direct solution of general third-order ordinary differential equations' initial value problems (IVPs). For the solution of IVPs, the power series functions were utilized as the basis function. To determine the unknown parameters, an approximate solution from the basis function was interpolated at chosen off-grid points. The third derivative of the estimated solution was collocated at all grid and off-grid points to produce a system of linear equations. Consistency, zero stability, convergence, and absolute stability were all evaluated on the method. The numerical results achieved through implementation are quite close to the theoretical solutions and compare well to other novel methods in the literature.
American Journal of Applied Mathematics and Statistics. 2022, 10(1), 4-13. DOI: 10.12691/ajams-10-1-2
Pub. Date: March 08, 2022
2085 Views2 Downloads
by Michael Gr. Voskoglou
Original Research
From the time that Zadeh introduced the concept of fuzzy set in 1965 a lot of research has been carried out for generalizing and extending the corresponding theory on the purpose of tackling more effectively the existing in real life uncertainty. One such generalization is the concept of soft set aiming, among others, to overcome the existing difficulty of defining properly the membership function of a fuzzy set. A new model using soft sets is presented in this paper for assessing human-machine performance in a parametric manner and examples are given to illustrate its applicability in practice. Such kind of models are very useful when the assessment has qualitative rather than quantitative characteristics.
American Journal of Applied Mathematics and Statistics. 2022, 10(1), 1-3. DOI: 10.12691/ajams-10-1-1
Pub. Date: January 09, 2022
1895 Views2 Downloads