Good exact confidence sets for a multivariate normal mean

Minimum Volume Confidence Regions for a Multivariate Normal Mean Vector

Since Stein’s original proposal in 1962, a series of papers have constructed confidence regions of smaller volume than the standard spheres for the mean vector of a multivariate normal distribution. A general approach to this problem is developed here, and used to calculate a lower bound on the attainable volume. Bayes and fiducial methods are involved in the calculation. Scheffe-type problems ...

Exact maximum coverage probabilities of confidence intervals with increasing bounds for Poisson distribution mean

 ‎A Poisson distribution is well used as a standard model for analyzing count data‎. ‎So the Poisson distribution parameter estimation is widely applied in practice‎. ‎Providing accurate confidence intervals for the discrete distribution parameters is very difficult‎. ‎So far‎, ‎many asymptotic confidence intervals for the mean of Poisson distribution is provided‎. ‎It is known that the coverag...

Screening for a Multivariate Mixture Normal Distribution

Exact hypothesis testing and confidence interval for mean of the exponential distribution under Type-I progressive hybrid censoring

 ‎Censored samples are discussed in experiments of life-testing; i.e‎. ‎whenever the experimenter does not observe the failure times of all units placed on a life test‎. ‎In recent years‎, ‎inference based on censored sampling is considered‎, ‎so that about the parameters of various distributions such as ‎normal‎, ‎exponential‎, ‎gamma‎, ‎Rayleigh‎, ‎Weibull‎, ‎log normal‎, ‎inverse Gaussian‎, ...

Multivariate Normal Distribution and Confidence Ellipses

the Normal Distribution's familiar "bell curve". The latter term can be interpreted as a description of squared of distance (x  between some value of x who's probability is being assessed (along the x axis), and  the center of the probability density distribution, "standardized" by the distribution's known variance 2. It should be noted that f(x) only depends on this single scalar range var...