Receiver operating characteristic (ROC) curves can be used to assess the accuracy of tests measured on ordinal or continuous scales. The most commonly used measure for the overall diagnostic accuracy of diagnostic tests is the area under the ROC curve (AUC). A gold standard (GS) test on the true disease status is required to estimate the AUC. However, a GS test may sometimes be too expensive or...

In this paper we present a new method to find simple or multiple roots of functions in a finite interval. In this method using bisection method we can find an interval such that this function is one to one on it, thus we can transform problem of finding roots in this interval into an ordinary differential equation with boundary conditions. By solving this equation using collocation method we ca...

In most applications, the data may be interval-censored. By interval-censored data, we mean that a random variable of interest is known only to lie in an interval, instead of being observed exactly. In such cases, the only information we have for each individual is that their event time falls in an interval, but the exact time is unknown. A nonparametric estimate of the survival function can al...

Interval arithmetic was original developed to estimate rounding errors on floating-point computations but it is used in a wide variety of applications from constraint solvers and global optimizers to power and timing analysis of software processes. The objective of interval analysis is to determine the output ranges (or interval) of a computation set. The main problem of classical interval anal...