Open Access Short Research Article

Integro-differential Equations for a Class of Delayed Renewal Risk Processes with Dependence

Shiyu Song

Asian Journal of Probability and Statistics, Page 48-61
DOI: 10.9734/ajpas/2022/v16i430409

The Gerber-Shiu discounted penalty function is considered for a class of delayed renewal risk processes. In (Willmot 2004), special cases of the model include the stationary renewal risk model and the situation where the time until the first claim is exponentially distributed. In this paper, we consider a class of delayed and perturbed risk model with dependence between interclaim arrivals and claim sizes. The integro-differential equations for the Gerber-Shiu discounted penalty functions are derived.

Open Access Short Research Article

On an Erlang(2) Process with Dependence Structure between Interclaim Arrivals and Claim Sizes

Qiao Li, Zhenhua Bao

Asian Journal of Probability and Statistics, Page 62-76
DOI: 10.9734/ajpas/2022/v16i430410

This paper considers an extension to the classical compound Poisson risk model for which an Erlang(2) process is utillized to the dependence structure between the claim sizes and interclaim times. In this framework, we derive the Lundberg generalised equation and the number of its roots, and the Laplace Transform(LT) of the expected discounted penalty function. We also show that the Gerber-Shiu function satisfies a defective renewal equation. Some explicit expressions are given to measure the impact of Erlang(2) dependence structure in the risk model on the ruin probability.

Open Access Original Research Article

Attributable Fraction and Forecasting for COVID-19 Confirmed Cases in Nigeria Using Facebook- Prophet Machine Learning Model

Olayemi Joshua Ibidoja, Kayode Rapheal Fowobaje

Asian Journal of Probability and Statistics, Page 1-10
DOI: 10.9734/ajpas/2022/v16i430406

Aims: The motivation is to know the attributable fraction among Nigerians who tested positive for covid-19 and forecast the covid-19 cases.

Place and Duration of Study: We extracted data from ( on 8th September,2021 and covid.19analytics package on 7th September, 2021, from Data Repository by Johns Hopkins University Center for Systems Science and Engineering , Status of Cases in Toronto – City of Toronto , COVID-19: Open Data Toronto ,COVID-19: Health Canada , Severe acute respiratory syndrome coronavirus 2 isolate Wuhan-Hu-1, COViD-19 Vaccination and Testing records from “Our World In Data” and Pandemics historical records from Visual Capitalist. Data in Nigeria contained the number of samples tested, confirmed cases, active cases, discharged cases and deaths.

Methodology: Attributable fraction was used to compute the proportion of patients who tested positive to Covid-19. By using the time for regressor, Prophet model will fit many non-linear and linear functions of time components. Prophet uses the Fourier series to get flexible model to forecast and fit the seasonality effects. A fast solution for L-BFGS which stands for Limited memory Broyden-Fletcher-Goldfarb-Shannon algorithm, is used with Stan backend for the prediction problem.

Results: As at Saturday 11th September 2021,7:18am Nigeria local time, a total of 2884034 samples have been tested for covid-19, with 198239 confirmed cases,9871 active cases,185780 discharged cases and 2588 deaths. The attributable fraction for covid-19 in Nigeria was 0.0687. The r square is very high (0.999), and the p value is very low (2.2e-16).

Conclusion: The attributable fraction gives the percentage of the patients who tested positive to covid-19, among the 2884034 samples tested. It implies that the remaining percentage of patients who tested negative to covid-19 only exhibit covid-19 symptoms or were exposed to the virus. The confirmed cases were found to be highest on Saturdays with the lowest on Tuesdays.

Open Access Original Research Article

An A- Stable Block Integrator Scheme for the Solution of First Order System of IVP of Ordinary Differential Equations

Muhammad Abdullahi, Shamsuddeen Suleiman, Abdu Masanawa Sagir, Bashir Sule

Asian Journal of Probability and Statistics, Page 11-28
DOI: 10.9734/ajpas/2022/v16i430407

In this article, we present an A- stable block integrator scheme for the solution of first order system of IVP of ordinary differential equations. The block scheme at a single integration step produces four approximate solution values of yn+1, yn+2, yn+3 and yn+4 at point xn+1, xn+2, xn+3 and xn+4 respectively. The order and stability property of the scheme are checked, the method is zero stable, A–stable and of order 6. Some test problems are solved with the proposed scheme and the result are compared with some existing method. The proposed method found to have advantages in terms of accuracy, minimum errors and less computational time. Hence, the method is recommended for solving first order system of IVP of ordinary differential equations.

Open Access Original Research Article

Time Delay in Engagement Schedules in a Public University in Ghana

Emmanuel Asare Ayim, John Awuah Addor, Frank B. K. Twenefour, Emmanuel M. Baah

Asian Journal of Probability and Statistics, Page 29-47
DOI: 10.9734/ajpas/2022/v16i430408

This paper aims to examine the incidence of time delays in engagement schedules on campus. The study made use of past records of time delays in starting committee meetings of five colleges at a public university in Ghana. The study relied on secondary data extracted from minute and agenda files of college meetings. The Minitab package and Microsoft Spreadsheet were used to analyse the data. The statistical techniques used in the study were Markov prosses and Steady state probability. The results revealed that the College of Agriculture and Natural Sciences consistently start their meetings on-time in the long-run with the highest probability of approximately 0.810. Meetings of the College of Education is characterized with large delays in starting times in the long-run with the highest probability of approximately 0.812. Based on the results, the paper recommends that the colleges with higher possibility of starting their meetings ten minutes late should encourage its board or committee members to be prompt in attending to meeting/schedules. Additionally, the paper suggests that the management of the university should design an effective policy to ensure a rescheduling when a meeting delays for more than an hour.

Open Access Original Research Article

The Influence of Measurement Errors on Generalized Estimator of Population Mean

Okafor, Ikechukwu Boniface, Onyeka Aloysius Chijioke, C. J. Ogbonna, Izunobi Chinyeaka Hostensia, Kiwu Lawrence Chizoba

Asian Journal of Probability and Statistics, Page 77-92
DOI: 10.9734/ajpas/2022/v16i430418

This paper proposed a generalized estimator of population mean in the presence of correlated and uncorrelated measurement errors under simple random strategy.  Some known estimators belong to this class of proposed estimator.  Under the large sample approximation, the properties of the proposed estimator namely bias and mean squared error were obtained. Theoretical comparison was carried out on the members of the proposed class of estimators when measurement errors are correlated and when they are uncorrelated and the necessary conditions under which the proposed estimator at its optimum value is expected to be more efficient than the existing estimators of finite population mean were obtained.  It was observed that correlated and uncorrelated measurement errors inflate the bias and mean squared error of the proposed estimator. The paper concluded that the proposed estimator is more efficient than usual unbiased estimator  and some members of the class of proposed estimator.