Comparisons of Approximate Confidence Intervals for Distributions Used in Life-Data Analysis

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.This article evaluates the accuracy of approximate confidence intervals for parameters and quantiles of the smallest extreme value and normal distributions. The findings also apply to the Weibull and the lognormal distributions. The interval estimates are based on (a) the asymptotic normality of the maximum likelihood estimator, (b) the asymptotic X2 distribution of the likelihood ratio (LR) statistic, (c) a mean and variance correction to the signed square roots of the LR statistic, and (d) the Bartlett correction to the LR statistic. The extensiveMonte Carlo results about true error probabilities and average lengths under various degrees of censoring show advantages of the LR-based intervals. For complete or moderately censored samples, the mean and variance correction to the LR statistic gives nearly exact and symmetric error probabilities. In small samples with heavy censoring, the Bartlett correction tends to give conservative error probabilities, whereas the uncorrected LR interval is often anticonservative. The results also indicate that LR-based methods have longer interval lengths than intervals based on the asymptotic normality of the maximum likelihood estimator.

Assessing the performance of the log-normal distribution with left truncated survival data

“…According to [9,10] the asymmetric (AS), conservative (C) and anticonservative (AC) confidence intervals for N=2000 with the nominal probability error (npe), 05 . 0 Į can be determined using (5) as follows.…”

Inferential Procedures for Log Logistic Distribution with Doubly Interval Censored Data

“…Following Doganaksoy & Schmee (1993), the interval is called anticonservative if the total error probability is more than α + 2.58se( â ). If the total error probability is less than α − 2.58se( â ), the interval is called conservative.…”

Vol. 16, No. 2 (Full Issue)

“…The left and right error probabilities were estimated and the total error probability was calculated. Following Arasan & Lunn (2009) and Kiani & Arasan (2013), the estimated left (right) error probability was obtained by summing up the numbers for the left (right) endpoint which was more (less) than the true parameter value divided by the total number of samples, N. The estimated total error probability was calculated by summing up the number of times in which an interval did not contain the true parameter value divided by N.The estimated error probabilities for Wald, likelihood ratio and jackknife intervals are given in Equations (28), (29) Following Doganaksoy & Schmee (1993), the interval is called anticonservative if the total error probability is more than α + 2.58se( â ). If the total error probability is less than α − 2.58se( â ), the interval is called conservative.…”