Search results
Results From The WOW.Com Content Network
The Nelson–Aalen estimator is a non-parametric estimator of the cumulative hazard rate function in case of censored data or incomplete data. [1] It is used in survival theory, reliability engineering and life insurance to estimate the cumulative number of expected events.
For instance, if estimating the effect of a drug on blood pressure with a 95% confidence interval that is six units wide, and the known standard deviation of blood pressure in the population is 15, the required sample size would be =, which would be rounded up to 97, since sample sizes must be integers and must meet or exceed the calculated ...
Some authors use the term Cox proportional hazards model even when specifying the underlying hazard function, [14] to acknowledge the debt of the entire field to David Cox. The term Cox regression model (omitting proportional hazards) is sometimes used to describe the extension of the Cox model to include time-dependent factors. However, this ...
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.
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".
The confidence interval can be expressed in terms of statistical significance, e.g.: "The 95% confidence interval represents values that are not statistically significantly different from the point estimate at the .05 level." [20] Interpretation of the 95% confidence interval in terms of statistical significance.
Cochran's test, [1] named after William G. Cochran, is a one-sided upper limit variance outlier statistical test .The C test is used to decide if a single estimate of a variance (or a standard deviation) is significantly larger than a group of variances (or standard deviations) with which the single estimate is supposed to be comparable.
Classically, a confidence distribution is defined by inverting the upper limits of a series of lower-sided confidence intervals. [15] [16] [page needed] In particular, For every α in (0, 1), let (−∞, ξ n (α)] be a 100α% lower-side confidence interval for θ, where ξ n (α) = ξ n (X n,α) is continuous and increasing in α for each sample X n.