Search results
Results from the WOW.Com Content Network
The colored lines are 50% confidence intervals for the mean, μ. At the center of each interval is the sample mean, marked with a diamond. The blue intervals contain the population mean, and the red ones do not. In statistics, a confidence interval (CI) is a tool for estimating a parameter, such as the mean of a population. [1]
For a confidence level, there is a corresponding confidence interval about the mean , that is, the interval [, +] within which values of should fall with probability . Precise values of z γ {\displaystyle z_{\gamma }} are given by the quantile function of the normal distribution (which the 68–95–99.7 rule approximates).
Comparison of the rule of three to the exact binomial one-sided confidence interval with no positive samples. In statistical analysis, the rule of three states that if a certain event did not occur in a sample with n subjects, the interval from 0 to 3/ n is a 95% confidence interval for the rate of occurrences in the population.
A confidence interval states there is a 100γ% confidence that the parameter of interest is within a lower and upper bound. A common misconception of confidence intervals is 100γ% of the data set fits within or above/below the bounds, this is referred to as a tolerance interval, which is discussed below.
This statistics -related article is a stub. You can help Wikipedia by expanding it.
when the probability distribution of the value is known, it can be used to calculate an exact confidence interval; when the probability distribution is unknown, Chebyshev's or the Vysochanskiï–Petunin inequalities can be used to calculate a conservative confidence interval; and
A great advantage of bootstrap is its simplicity. It is a straightforward way to derive estimates of standard errors and confidence intervals for complex estimators of the distribution, such as percentile points, proportions, Odds ratio, and correlation coefficients.
Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.