Asian Journal of Probability and Statistics

The mathematical study of waiting lines is mainly concerned with queue performance measures where several applications have been drawn in past studies. Among the vast uses and applications of the theory of queuing system in banking halls, is the main focus of this study where the theory has been used to solve the problem of long queues as witnessed in banks leads to resource waste. The study aims to model the waiting times for queues in selected banks within Eldoret town, Kenya. The latter component was put under D/D/1 framework and therein its mean derived while the stochastic component was put under the M/M/c framework. Harmonization of the moments of the deterministic and the stochastic components was done to come up with the mean of the overall bank queue traffic delay. The simulation was performed using MATLAB for traffic intensities ranging from 0.1 to 1.9. The results reveal that both deterministic and the stochastic delay components are compatible in modelling waiting time. The models also are applicable to real-time bank queue data whereupon simulation, both models depict fairly equal waiting times for server utilisation factors below 1 and an infinitely increasing delay at rho greater than 1. In conclusion, the models that estimate waiting time were developed and applied on real bank queue data. The models need to be implemented by the banks in their systems so that customers are in a position to know the expected waiting time to be served as soon as they get the ticket from the ticket dispenser.

Rotatability is a desirable feature of a response surface experimental design. In case a design is non rotatable or exhibit surface of constant prediction variances that are nearly spherical then an attempt is made to make the design rotatable. In this paper, a measure of rotatability of five level second order rotatable designs using an infinite class of supplementary difference sets is suggested. The variance function of a second-order response design and an infinite class of supplementary difference sets is used in coming up with the design.

For mood State and Behavior Predictions in Social Media through Unstructured Data Analysis, a new model, Behavior Dirichlet Probability Model (BDPM), which can capture the Behavior and Mood of user on Social media is proposed using Dirichlet distribution. There is a colossal amount of data being generated regularly on social media in the form of text from various channels by individuals in the form of posts, tweets, status, comments, blogs, reviews etc. Most of it belongs to some conversation where real-world individuals discuss, analyze, comment, exchange information. Deriving personality traits from textual data can be useful in observing the underlying attributes of the author’s personality which might explain a lot about their behavior, traits etc. These insights of the individual can be utilized to obtain a clear picture of their personality and accordingly a variety of services, utilities would follow automatically. Using Dirichlet probability distribution, the aim is to estimate the probability of each personality trait (or mood state) for an author and then model the latent features in the text which are not captured by the BDPM. As a result, the study can be helpful in prediction of mood state/personality trait as well as capturing the significance of the latent features apart from the ones present in the taxonomies, which will help in making an improved mood state or personality prediction.

This paper presents the solutions to the equations governing convective flow and heat transfer of two viscous immiscible dusty and pure fluids confined between a vertical corrugated wall and a parallel flat wall. The nonlinear partial differential equations governing the flow have been reduced to nonlinear ordinary differential equations using the regular perturbation method. The transformed nonlinear ordinary differential equations have been solved numerically using the linear approximation theorem. The effects of the governing parameters on the velocity and temperature fields for the two fluids and the dust particles have been obtained and graphically represented using Matlab.

Background: In linear time series, the in-sample model selection and the out-of-sample model selection are the two common approaches to model selection. However, empirical evidence based on out-of-sample forecast performance is generally considered more trustworthy than evidence based on in-sample performance, which is deficient in providing information about future observations.

Aim: The aim of the study is to select the best linear time series model suitable to predict Nigeria exchange rates for the period 2002-2018.

Materials and Methods: Data on naira to pound and naira to euro exchange rates from January 2002 to December 2018, comprising of 204 data points were considered. The data were divided into two portions; the first portion which comprises of 192 observations was used for model building while the second portion with 12 observations was used for out-of-sample prediction evaluation. The Box-Jenkins ARIMA iterative procedure was used in model building while the mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and Theil’s U coefficient were the measures of accuracy adopted in selecting the best out-of sample model.

Results: Our results revealed that, based on in-sample model selection, ARIMA (0, 1, 1) and ARIMA (1, 1, 0) were the appropriate models with minimum information criteria. However, on the basis of out-sample forecast performance evaluation criteria, ARIMA (1, 1, 0) and ARIMA (1, 1, 2) were found to be appropriate out-of-sample models with minimum forecast evaluation criteria. In all, our results showed that, the out-of sample models performed better than their in-sample counterparts in their ability to forecast future values.

Conclusion: So far, this study revealed that out-of-sample is a better model selection criterion than the in-sample counterpart as evident in its ability to predict future values which is the very essence for modelling in time series.