The dose-response phenomenon characterized by low dose stimulation and high dose toxicity has been reawakened after a long period of marginalization. This phenomenon termed hormesis is induced by biological, physical and chemical agents and occurs in all groups of living things including whole plants and animals, microorganisms, cells and tissues. Hormesis has attracted increased interest among toxicologists from diverse disciplines, resulting to emergence of new scientific tools for its study. Statistical models have been developed and used to characterize hormesis dose-response relationships. Some of these models include the classical Brain-Cousens model, the Cedergreen-Ritz-Streibig model and their reparameterizations. Other hormesis models are the bilogistic models, their modifications or extensions and the hormesis models used in allelopathy such as An-Johnson-Lovett model. These models are used to describe either U-shaped or inverted U-shaped dose-response relationships and to compute hormesis quantities. This review explored the applications of these models in toxicological studies with emphasis to their strengths and weaknesses.

In this study, we developed multivariate model for the study of the impact of treasury single account (TSA) on the performance of banks in Nigeria. From the study, we discovered that there was no significant difference between the period before and after the introduction of the TSA policy on the performance of banks in Nigeria. In Diamond Bank Nigeria Plc, we observed that there were negative relationships between liquidity ratio and capital adequacy with correlation coefficient of −0.093; liquidity ratio and credit to customers with correlation coefficient of −0.312; capital adequacy and credit to customers with correlation coefficient of −0.176. On the other hand, from the analysis on first bank, we observed that there were both positive and fairly strong relationships between the liquidity ratio and capital adequacy with correlation coefficient of 0.626; negative relationship between liquidity ratio and credit to customers with correlation coefficient of −0.880 and finally, negative relationship between capital adequacy and credit to customers with correlation coefficient of −0.165.

Having lectured in some universities and polytechnics in Nigeria, the researchers observed problems in course allocations. There are no lay-down techniques on how courses should be allocated with respect to the minimum and maximum credit a lecturer should carry in a semester. Many lecturers were overloaded while others were under-loaded. For this reason, dynamic programming model was developed for allocating courses among lecturers in the Nigerian universities using the Department of Statistics, Federal University of Technology Owerri, as a case study. From our analysis, we observed that among all the optimal allocations discovered in the study, the best optimal allocation policy was achieved at the point (1, 2, 1, 2). Allocation of courses in this order will yield an optimal credit hour of 12 per lecturer per semester.

Prostrate cancer has been observed to be a worrisome ailment among adult males across the globe over some decades. Just like any other ailment, its early detection and treatment gives the patient a better chance of survival. Measuring the Prostrate specific antigen (PSA) of the patients at specified intervals is one of the techniques of detecting the onset of prostrate cancer. This paper attempts to obtain the most appropriate probability distribution of prostrate specific antigens (PSA) that gives the best estimates of the parameters of the distribution. The age specific probabilities of patients with prostrate specific antigen (PSA)>4.0ng/ml were calculated. The results show that the most appropriate distribution among the distributions fitted is the Burr distribution. The probability of observing a PSA greater than 4.0 ng/ml in adult males above the age of 45 years was seen to be moderately high (0.68) with a median PSA of 8.30 ng/ml and an inter quartile range of 16.40. The results also show that PSA of 60.0 ng/ml and above were exceptional cases that require urgent attention. It was observed that men whose ages are between 60 and 80 years have higher chances of having PSA values greater 4.0ng/ml with men between 60 and 75 years having the highest chances. It is therefore suggested that men with PSA higher than 4.0ng/ml between 60 and 80 years of age may not be subjected to needle biopsies but be referred directly for digital rectal examinations.

Water scarcity is the major problem confronting both urban and rural dwellers in Enugu State. This scarcity emanated from indiscriminate pipe failure, lack of adequate maintenance, uncertainty on the time of repair or replacement of pipes etc. There is no systematic approach to determining replacement or repair time of the pipes. Hence, the rule of thumb is used in making such a vital decision. The population is increasing, houses are built but the network is not expanded and the existing ones that were installed for no less than two to three decades ago are not maintained. These compounded the problem of scarcity of water in the state. Replacement or repair of water pipes when they are seen spilling water cannot solve this lingering problem. The solution can be achieved by developing an adequate predictive model for water pipe replacement. Hence, this research is aimed at providing a solution to this problem of water scarcity by suggesting a policy that will be used for better planning. The interests in this paper were to obtain a water pipe failure model, the intensity function λ(t) [failure rate], the reliability R(t) and the optimal time of replacement and they were achieved. It was observed that the failure rate of the pipes increases with time while their reliability deteriorates with time. Hence, the Optimal replacement policy is that each pipe should be replaced after 4 th break when the reliability = 0.0011.