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Fiducial confidence limits and prediction limits for a gamma distribution: Censored and uncensored cases
Author(s) -
Krishnamoorthy Kalimuthu,
Wang Xiao
Publication year - 2016
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.2408
Subject(s) - percentile , confidence interval , statistics , cube root , fiducial marker , coverage probability , mathematics , monte carlo method , sample (material) , computer science , artificial intelligence , chemistry , geometry , chromatography
The problems of finding confidence limits for the mean and an upper percentile, and upper prediction limits for the mean of a future sample from a gamma distribution are considered. Simple methods based on cube root transformation and fiducial approach are proposed for constructing confidence limits and prediction limits when samples are uncensored or censored. Monte Carlo simulation studies indicate that the methods are accurate for estimating the mean and percentile and for predicting the mean of a future sample as long as the percentage of nondetects is not too large. Algorithms for computing confidence limits and prediction limits are provided. Necessary R programs for calculating confidence limits and prediction limits are also provided as a supplementary file. The methods are illustrated using some real uncesnored/censored environmental data sets.