Asian Journal of Probability and Statistics

Box and Hunter [1] introduced the concept of rotatability for response surface designs. The concept of slope-rotatability was introduced by Hader and Park [2] as an analogous to rotatability property, which is an important design criterion for response surface design. Slope-rotatable design is that of which the variance of partial derivative is a function of distance from the design (d). Recently, a few measures of slope-rotatability for a given response surface design was introduced. In this paper, a new method of slope rotatability for second order response surface designs under tri-diagonal correlation structure of errors using a pair of symmetrical unequal block arrangements with two unequal block sizes is studied. Further, a study on the dependence of variance function of the second order response surface at different design points for different values of tri-diagonal correlation coefficient ρ which lies between -0.9 to 0.9 and the distance from centre (d) is suggested.

The stock market in an emerging country like Pakistan has been volatile from the earliest times. This paper studies the volatility of Pakistan Stock Exchange (PSX) (using Karachi Stock Exchange 100 Index (KSE-100) as a proxy) through the application of Generalized Autoregressive Conditional Heteroscedasticity (GARCH) family models.

The sample period consists of 4831 daily observations for the 19 year trading period (from 2000 to 2019). Symmetric GARCH (2, 1), asymmetric EGARCH (1, 1), GJR-GARCH (1, 1) and APARCH (1, 1) models were used under Gaussian distributional assumptions. The results validate the empirical findings of previous studies conducted in Pakistan that log returns of KSE-100 Index are characterized by volatility clustering, time-variability, leptokurtic distribution with dominant ARCH and GARCH effects. An interesting feature of Pakistan Stock Exchange revealed by asymmetric models (used in the study) is that PSX is more volatile to good news than bad news. Moreover EGARCH (1, 1) outperforms all other models of the study on the basis of AIC/BIC criterion. However the comparison of correlations of variances predicted by three asymmetric models reveal that correlations among them are very high, with minimum correlation being 98%. This essentially means that all three asymmetric models provide a good fit to PSX.

In this paper, we review some estimators of count regression (Poisson and negative binomial) models in panel data modeling.  These estimators based on the type of the panel data model (the model with fixed or random effects). Moreover, we study and compare the performance of these estimators based on a real dataset application. In our application, we study the effect of some economic variables on the number of patents for seventeen high-income countries in the world over the period from 2005 to 2016. The results indicate that the negative binomial model with fixed effects is the better and suitable for data, and the important (statistically significant) variables that effect on the number of patents in high-income countries are research and development (R&D) expenditures and gross domestic product (GDP) per capita.

Aim: We evaluate the performance of parametric models, mixture of generalized gamma frailty model with Gompertz distribution and compare it with Cox proportional hazard model that is commonly used in the analysis of TB patients and also by [1].

Place and the Duration of the Study: The study was carried out in Bauchi State, Nigeria from January, 2017 to January, 2020.

Methodology: In this study secondary data was used and gotten from the patients’ treatment card and TB registers from January 2015 to December 2017. The covariates used were, drug, age, marital status, smoking habit, educational level, weight, category, and risk factor. We used AIC and BIC selection tool to select the model with the lowest value and then compare it with Cox hazard model. Data analysis was done in Stata version 14.

Results: The result of the analysis shows that mixture of frailty model with Gompertz baseline distribution has the lowest AIC and BIC value when compared to Cox Proportional model therefore shows a better goodness of fit for our dataset.

Conclusion: We therefore conclude that mixture of frailty model with Gompertz baseline distribution model can serve as an alternative to Cox Proportional Model.

The purpose of this paper is to find out the operating characteristics of the ATM service point of the Fidelity bank Plc, plateau state. Specifically, a computer package (MS60) was used for analyzing the data. Results obtained from the analysis showed the traffic intensity (ρ) to be 0.96, which indicated that the service facility is highly utilized. The average length of the queue was found to be 21 while the average waiting time in the queue was 1.10 hours. On the basis of this investigation, the conclusion was made that the service utility is highly utilized, implying that there are more customers than the service point can accommodate thus giving rise to the lengthy customer waiting time. It is recommended that one additional ATM be deployed to the bank's premises so as to minimize customer waiting time and to also increase the service rate.