It is computed by ordering the PI across patients, calculating the rankits (expected standard normal order statistics) corresponding to these values, dividing the latter by a factor κ = 8 / Π ≃ 1. 596 and performing Cox regression on the scaled rankits.
Standard deviations, higher order statistics, and Hjorth mobility and complexity parameters [13 15] for each system's signals were also examined.
The data did not resemble a Gaussian distribution, if the data lay outside of the confidence envelopes based on the standard errors of order statistics for an independent sample from the Gaussian distribution.
On the other hand, by taking such frequency as one of the weight factors and integrating variance of order statistics under standard distribution, weighted least square estimation is formed for accurately estimating various censoring samples.
For a better stability, instead of sample standard deviations, we used the corresponding order statistics, namely, the difference of quantiles: (25) For Gaussian distributions, this quantity (Eq. (25)) coincides with its standard deviation (SD).
Monte Carlo simulation (MCS) is used to obtain the second order statistics (mean value and standard deviation) of the pull-in voltage.
Using Monte Carlo simulation, the second order statistics i.e., mean and standard deviation of the nonlinear free vibration response of the composite laminates are obtained for different thickness and amplitude ratios.
An improved set of plotting positions based on the mean values of the order statistics are derived, together with a means of obtaining the standard deviation of each position.
The Wan et al. estimator of the standard deviation is based on normality assumption and uses approximation of expected values of the order statistics.
For example, simple substitution methods, parametric methods, nonparametric Kaplan-Meier methods, and robust regression on order statistics methods can be used to obtain summary statistics (e.g., means, standard deviations, medians, and percentiles) for left-censored data.
