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estimate the EPC term. The basis and theoretical justification for those recommendations are <br /> summarized in Singh and Singh(2003)for full data sets without ND observations. <br /> UCLs for Full Uncensored Data Sets without ND Observations <br /> 1. Student's-t UCL: to be used for normally (or at least approximately normally) distributed <br /> data sets. Student's-t UCL is available for all confidence coefficients, (1-a) in the interval <br /> [0.5, 1.0). <br /> 2. Approximate Gamma UCL: to be used for gamma distributed data and is typically used <br /> when k hat(ML estimate of the shape parameter,k) is greater than or equal to 0.5. <br /> Approximate gamma UCL is available for all confidence coefficients (1-a) in the interval <br /> [0.5, 1.0). <br /> 3. Adjusted Gamma UCL: to be used for gamma distributed data sets and should be used <br /> when k hat is greater than 0.1 and less than 0.5. Adjusted gamma UCL is available only <br /> for three confidence coefficients: 0.90, 0.95, and 0.99. <br /> 4. H-UCL based upon Land's H-statistic: to be used for lognormally distributed data sets. In <br /> ProUCL, H-UCL is available only for two confidence coefficients: 0.90 and 0.95. <br /> ProUCL can compute H-UCL for samples of size up to 1001. <br /> Caution: For highly skewed data sets,the use of H-UCL should be avoided as the H- <br /> statistic often results in unrealistically large, impractical and unusable H-UCL values. <br /> ProUCL provides warning messages and recommends the use of alternative UCLs for <br /> such highly skewed lognormally distributed data sets. <br /> 5. Chebyshev (MVUE) UCL: to be used for lognormally distributed data sets. This UCL <br /> computation method uses the MVU estimates of the standard deviation of the mean and <br /> of other parameters of a lognormal distribution. Chebyshev (MVUE) UCL is available <br /> for all confidence coefficients, (1-a) in the interval [0.5, 1.0). <br /> 6. Central Limit Theorem(CLT)based UCL: to be used when the sample size is large. <br /> 7. Adjusted-CLT (adjusted for skewness)UCL: may be used for mildly skewed data sets of <br /> large sizes. <br /> 8. Modified-t statistic (Adjusted for skewness)based UCL: may be used for mildly skewed <br /> data. <br /> Caution: UCLs listed in 6, 7, and 8 do not provide adequate (e.g., 95%) coverage when <br /> the data are moderately to heavily skewed, even when the sample size is large such as <br /> greater than 50. <br /> 9. Chebyshev(Mean, Sd)UCL: based upon the sample mean and standard deviation, Sd. <br /> 10. Jackknife UCL for mean(same as Student's-t UCL). <br /> 11. Standard Bootstrap UCL. <br /> 12. Bootstrap-t UCL. <br /> 13. Hall's Bootstrap UCL. <br /> 14. Percentile Bootstrap UCL. <br /> 15. Bias-corrected accelerated(BCA) Bootstrap UCL. <br /> UCLs Based Upon Left Censored Data Sets with ND Observations <br /> In order to compute UCLs, one has to first obtain estimates of population mean, standard <br /> deviation, and standard error of the mean based upon data sets with single or multiple detection <br /> limits. ProUCL 4.0 has a couple of estimation methods such as the ROS methods and Kaplan- <br /> Meier(KM)method that can handle multiple detection limits. The following methods for <br /> estimation of population mean and the standard deviation have been incorporated in ProUCL 4.0 <br />