Open Access Case Study

An Application of Single and Multi-server Exponential Queuing Model in Some Selected Hospitals of the North-Western Nigeria

Shamsuddeen Suleiman, Muhammad Sani Burodo, Zubairu Ahmed

Asian Journal of Probability and Statistics, Page 1-9
DOI: 10.9734/ajpas/2022/v16i230396

Time spent by patients to get service at the hospital is becoming a major source of concern to health care providers. The results of keeping patients waiting for too long in a queue in order to assess medical services may put them in so many inconveniences or at times can lead to congestion. Also, providing too much service capacity to operate a system incurs excessive cost. But not providing enough service capacity results in excessive waiting time and cost. This brings the need to strike a balance between excessive waiting time and cost. To achieve this, multi-server exponential queuing system was adopted and applied. The queuing performance characteristics were calculated with help of Microsoft Excel package. The data for this study were collected from eight hospitals across Katsina, Kaduna, Sokoto and Zamfara States in North-Western Nigeria through observations and personal interview. The results reveal that the General hospital Hunkuyi is the busiest because it has recorded the highest utilization factor as well as the highest number of patients in the queue. However, Ahmadau Bello University, Teaching hospital, Zaria is the least busy hospital and Federal medical centre, Katsina has the lowest number of patients in the queue.

Open Access Short Research Article

The F- Distribution with Applications to Number of Female Patients with Cancer

E. K. Akinyemi, O.A. Ogunsola, B. O. Oyinbodunmi

Asian Journal of Probability and Statistics, Page 10-14
DOI: 10.9734/ajpas/2022/v16i230397

The F-distribution is a particular parameterization of the beta prime distribution, which is also called the beta distribution of the second kind. This considered a new four-parameter generalized version of the Fisher Snedecor distribution called Beta- F distribution is introduced. The comprehensive account of the statistical properties of the new distributions was considered. Formal expressions for the cumulative density function, moments, and moment generating function and maximum likelihood estimation as well as its Fisher information were obtained.

 This study employed a descriptive survey research design. The target population was female patients with cancer in Lagos State University teaching Hospital for complete for 36 days.  The data collected was analyzed using both descriptive statistics and presented in tables, charts and figures. Some well-known distributions were fit, some existing single distributions and the proposed F distribution to these data using the method of maximum likelihood was applied using Micro-Soft Excel 2007.

The study established that the minimum AIC and minimum statistic on kolmogorov Smirnov of the F-distribution shows that female patients with cancer data better than the other life time distributions considered. The study concluded that Fisher-distribution is better off than existing single distribution with reference to Akaike Information Criterion (AIC) been used. It is instructive to note that the F-distribution preserves the originality of the data without transformation.

Open Access Original Research Article

Spatiotemporal Modelling of Endemic-epidemic Cholera in Nigeria

A. Usman, A. Isah, U. Abubakar, M. James

Asian Journal of Probability and Statistics, Page 15-24
DOI: 10.9734/ajpas/2022/v16i230398

This study used a multivariate negative binomial model to capture the Spatiotemporal endemic-epidemic of infectious disease and explore the spatial and temporal patterns of cholera outbreaks in Nigeria. The model for the epidemic part measured spatial weights for the disease spread across the geographical neighboring regions and the endemic part accounted for temporal variation of disease incidence. Weekly count data on cholera from the Nigeria Department of Disease Control and Monitoring Epidemiology (NCDC SED) between January 1st and November 19th, 2018 was used to illustrate the model. In fitting the model, the study has shown that the model with seasonality and autoregressive components provided an adequate fit for the cholera count data and also perform better than the model without seasonality and autoregression for modelling the Spatiotemporal dependency structure of cholera disease

Open Access Original Research Article

Bayesian Estimation of the Parameters of the Odd Generalized Exponentiated - Inverse Exponential Distribution (OGE -IED)

Treng Kirnan Gayus, Sani Ibrahim Doguwa

Asian Journal of Probability and Statistics, Page 25-36
DOI: 10.9734/ajpas/2022/v16i230399

The Odd Generalized Exponentiated-Inverse Exponential Distribution, a three parameter distribution, is a hybrid of the Generalized Exponential distribution. Each of the parameters were assigned a gamma prior independently resulting to a posterior distribution that is mathematically intractable impossible to obtain marginal posterior distribution for two of the parameters, and a likelihood function that is not known traditionally to R or other statistical software. Resort was made to STAN in order to obtain Bayesian estimates - leveraging on STAN’s provision for user-defined distribution functions. Two datasets were used; remission times (in months) of bladder cancer patients and COVID-19 Survey data in Andalusia, Spain. In the end, the Maximum Likelihood estimates maximized the likelihood more than the Bayesian estimates - though with a slight margin of not more than 0.77. On the other hand, the Bayesian estimates proved to be more stable yielding very negligible standard errors compared to the Maximum Likelihood estimates.

Open Access Original Research Article

Type II Topp Leone Generalized Inverted Exponential Distribution with Real Data Applications

Zakeia A. Al-Saiary, Sarah H. Al-Jadaani

Asian Journal of Probability and Statistics, Page 37-51
DOI: 10.9734/ajpas/2022/v16i230400

The generalization of standard and generalized distributions has become one of the concerns that the statistical theory depends on to obtain more exible distributions. In this article, a new distribution that is considered a generalization of the generalized inverted exponential distribution called the Type II Topp Leone Generalized Inverted Exponential (TIITLGIE) distribution is introduced. Some statistical properties of this distribution were obtained. The quantile function, median, moments, moment generating function, Reliability function, hazard function, mode, harmonic mean, mean and median deviation are derived. Furthermore, important measures such Rnyi entropy and the Maximum Likelihood (ML) estimation are deduced for parameters. Conduct a Monte Carlo simulation to study behavior of parameter estimates. Finally, applications on three real data sets are discussed.