Asian Journal of Mathematical Sciences(AJMS)

Review on the Inverse Rayleigh Distribution

Amel Abd-El- Monem — 2022-06-14

This article discusses Bayesian and non-Bayesian estimation problem of the unknown parameter for the inverse Rayleigh distribution based on the lower record values. Maximum likelihood estimators of the unknown parameters were obtained. Furthermore, Bayes estimator has been developed under squared error and zero one loss functions. We discuss also statistical properties and estimation of power-transmuted inverse Rayleigh distribution (EIRD). We introduce the transmuted modified inverse Rayleigh distribution using quadratic rank transmutation map, which extends the modified inverse Rayleigh distribution. We introduce a generalization of the inverse Rayleigh distribution known as EIRD which extends a more flexible distribution for modeling life data. Some statistical properties of the EIRD are investigated, such as mode, quantiles, moments, reliability, and hazard function. We describe different methods of parametric estimations of EIRD discussed by using maximum likelihood estimators, percentile-based estimators, least squares estimators, and weighted least squares estimators and compare those estimates using extensive numerical simulations. The new two-scale parameters generalized distribution were studies with its distribution and density functions, besides that the basic properties such as survival, hazard, cumulative hazard, quantile function, skewness, and Kurtosis functions were established and derived. To estimate the model parameters, maximum likelihood, and rank set sampling estimation methods were applied with real-life data. We have introduced weighted inverse Rayleigh (WIR) distribution and investigated its different statistical properties. Expressions for the Mode and entropy have also been derived. A comprehensive account of the mathematical properties of the modified inverse Rayleigh distribution including estimation and simulation with its reliability behavior is discussed.

On the Analytic Review of Some Contraction and Extension Results in the Hilbert Space with Applications in the Solution of Some Elasticity Problems

Eziokwu C. Emmanuel — 2022-07-12

This research reviews the analysis of contraction and extension maps in the Hilbert space through the spectral theory approach. Some very important results were discussed and illustrated fully the aid of which analytical works on contraction and extension was fully utilized in the applied mathematics of elasticity theory of various deformation problems as seen in section three of this work.

A Monte Carlo Study of Empirical Performance of Threshold Autoregressive Models on Nonlinear Non-Stationary

Alhaji Umar Abubakar — 2022-07-12

One of the major importance of modeling in time series is to forecast future values of that series which requires the use of appropriate method to fit the time series data that are dependent on the nature of the data. However, real-life data are mostly non-stationary and nonlinear. This will be a problem when a model is in appropriately applied to data that does not fits in, the result of the outcome will be inaccurate and this will not give the clear picture of what the data entails in the future events. In this study, the performances of the smooth transition autoregressive (STAR) and the self-exciting threshold autoregressive (SETAR) models of different orders and regimens were compared on different forms of nonlinear cases of autoregressive under violation of stationarity assumption. Simulated data with features of nonlinearity and non-stationarity were used to compare the performance of the models. The relative performances of the models were examined with a view to identify the best models at orders 1, 2, and 3, and regimen 2 when fitted to linear, trigonometric, exponential, and polynomial autoregressive functions. It was concluded that the SETAR (2, 1) is the best model followed by SETAR (2, 2) to fit linear data, whereas the SETAR (2, 2) and STAR (2, 3) are considered to be the best for an exponential and SETAR (2, 2) and STAR (2, 2) for a polynomial data.

A Mathematical Model for the Control on the Transmission Dynamics of COVID-19 Pandemic Containing Asymptomatic and Symptomatic Classes

O. A. Adedayo — 2022-07-12

In this research paper work, we developed a COVID-19 epidemic disease model fitted in Nigeria situation. In this model system, we divided Nigeria population into six subpopulations such as Susceptible population, Exposed population, Infected asymptomatic population, Infected symptomatic population, isolated symptomatic population, and the fully recovered population. Control measures parameter (hand sanitizers and nose masks) was incorporated into the model. We obtained the disease-free equilibrium and endemic equilibrium points. The basic reproduction number was obtained using the new generation matrix, the local and global stability was also obtained to be locally and globally asymptotically stable at R0<1 for the DFE. We did numerical simulations using (Maple 17) software. The results showed the importance of the control measures and social distancing through graph.

A Study on Selected Mathematical Theories for Decision-Making Problems

Sreelekshmi C. Warrier — 2022-07-12

The most appropriate mathematical theory for dealing with uncertainty in decision making problems, the theory of fuzzy set developed by Zedeh in 1965. Later in 1999, Molodstov introduced another one namely, soft set theory for modelling vagueness and uncertainty in decision making problems. In this paper, we study some mathematical tools such as fuzzy set, soft set and fuzzy soft set for solving decision making problems.

Mathematical Modeling for the Transmission Dynamics Control of HIV and Malaria Coinfection in Nigeria towards Attaining Millenium Development Goal

S. Ale — 2022-07-12

Human immune deficiency virus and malaria coinfection are among the greatest health problems globally and the understanding of how the two infections network could be imperative for the control of both diseases. Hence, this research formulated a mathematical model to study the coinfection of human immunodeficiency virus/acquired immunodeficiency syndrome and malaria in the presence of treatment as control measures. The basic reproduction number was obtained using the next generation matrix method. The simulations were carried out using MAPLE 18 software. The result shows that the malaria treatment does not have any effect on the total coinfected populations. Thus, every sick person should be tested to ascertain the source of their health challenges.

Application of Multi-server Queue Model (m/m/c) for Waiting Lines Management in Banking System

S. A. Akande — 2022-07-28

Queues or waiting lines arise when the demand for service exceeds the capacity of a service facility.
One of the major challenges bank customers encounter in banks is the waiting lines in automated teller
machines (ATMs). This study formulated a Multi-Server Queue Model (M/M/C) for Queue Management
in Banking ATM. The performance level of a typical bank ATM has been effectively investigated using
the M/M/S queuing model. It was observed that the busy time of the machine is 2.6 h while the idle time
is 7.4 h in the 10 h of banking time which is attributed to the availability of many servers in the system.
The utilization factor is 0.26 or 26.0% shows that the service delivery of the machine is very efficient and
there is no urgent need for an additional server. The researcher thereby recommended that banks should
consider the use of the queue model to test the performance of waiting lines in the ATMs.