BACKGROUND The ratio of two measured fluorescence signals (called x and y) is used in different applications in fluorescence microscopy. Multiple instances of both signals can be combined in different ways to construct different ratio estimators. METHODS The mean and variance of three estimators for the ratio between two random variables, x and y, are discussed. Given n samples of x and y, we...

We calculate the finite sample probability mass-at-zero and the probability of underestimating the true ratio between random effects variance and error variance in a LMM with one variance component. The calculations are expedited by simple matrix diagonalization techniques. One possible application is to compute the probability that the log of the likelihood ratio (LRT), or residual likelihood ...

Population quantiles are important parameters in many applications. Enthusiasm for the development of effective statistical inference procedures and their functions has been high past decade. In this article, we study methods when multiple samples from linked populations available. The research problems consider have a wide range For example, to evolution economic status country, economists mon...

Time-to-event endpoints show an increasing popularity in phase II cancer trials. The standard statistical tool for such one-armed survival trials is the one-sample log-rank test. Its distributional properties are commonly derived large sample limit. It however known from literature, that asymptotical approximations suffer when size small. There have already been several attempts to address this...

In this paper, we have proposed a class of ratio-cum-dual to ratio estimators using known values of some population parameters of the auxiliary variable to estimate the population variance of the study variable. The expressions for the bias and mean square error of the proposed estimators have been derived upto the first order of approximation. A comparison has been made with some well known es...