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a) The expression inside the square root has to be positive, or else the resulting interval will be imaginary. b) When g is very close to 1, the confidence interval is infinite. c) When g is greater than 1, the overall divisor outside the square brackets is negative and the confidence interval is exclusive.
In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a parameter of interest. This is in contrast to point estimation, which gives a single value. [1] The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method). [2]
In statistics, the Behrens–Fisher problem, named after Walter-Ulrich Behrens and Ronald Fisher, is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples.
The concept of fiducial inference can be outlined by comparing its treatment of the problem of interval estimation in relation to other modes of statistical inference. A confidence interval , in frequentist inference , with coverage probability γ has the interpretation that among all confidence intervals computed by the same method, a ...
Approximate estimate of the value range. The so-called "dependency" problem is a major obstacle to the application of interval arithmetic. Although interval methods can determine the range of elementary arithmetic operations and functions very accurately, this is not always true with more complicated functions.
In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated.This can be thought of as a generalisation of many classical methods—the method of moments, least squares, and maximum likelihood—as well as some recent methods like M-estimators.
a point estimate, i.e. a particular value that best approximates some parameter of interest; an interval estimate, e.g. a confidence interval (or set estimate), i.e. an interval constructed using a dataset drawn from a population so that, under repeated sampling of such datasets, such intervals would contain the true parameter value with the ...
This is not as much of a problem for intervals that are lower and upper bounds derived from a set of probability distributions, e.g., a set of priors followed by conditionalization on each member of the set. However, it can lead to the question why some distributions are included in the set of priors and some are not.