This paper offers a technique to construct a prediction interval for the future value of the last variable in the vector r of m variables when the number of observed values of r is small. Denoting r(t) as the time-t value of r, we model the time-(t+1) value of the m-th variable to be dependent on the present and l-1 previous values r(t), r(t-1), …, r(t-l+1) via a conditional distribution which is derived from an (ml+1)-dimensional power-normal distribution. The 100(α / 2)% and 100(1−α / 2)% points of the conditional distribution may then be used to form a prediction interval for the future value of the m-th variable. A method is introduced to estimate the above (ml+1)-dimensional power-normal distribution such that the coverage probability of the resulting prediction interval is nearer to the target value 1- α .
Objective: An in vitro assessment of MG-63 human osteosarcoma cells' alkaline phosphatase (ALP) activity when in contact with calcium hydroxide powder (CH), paste (CHP) and grey mineral trioxide aggregate (MTA). Methods: MG-63 cells were seeded to the three selected materials for durations of 0.25, 0.5, 1, 24, 48 and 72 hours. BCIP-NBT assay was used and ALP activity quantified using ELISA reader at 410 nm. Results: The overall analysis for ALP activity indicated significant interaction between test materials and control (maintenance medium). Subsequently, the test materials were paired and analysed for initial (0.25, 0.5, 1 hour) and delayed response (24, 48 and 72 hours). During the initial response, CH exhibited an increased ALP activity compared to MTA. This interaction was not dependant on duration. The delayed response exhibited elevated ALP activity with CHP when compared to MTA and CH. The interaction of CHP was dependant on duration. Conclusion: All three materials exhibited increased ALP activity.