Is there any software for calculating the factor for two sided tolerance limits for normal distribution for a given gamma and P.
For reference look at table IV.19 (page 573) in the Pharmaceutical Statistics Practical and Clinical Applications
http://ajprd.com/downloadebooks_pdf/28.pdf
In Excel the function is NORM.S.INV(.).
In R the function is qnorm(.).
In WolframAlpha (http://www.wolframalpha.com/) you can enter:
standard normal quantile of 0.025 probability
(you may exchange the probability value (here: 0.025) by any value for which you want to get the corresponding quantile.
Mohd,
the normal distribution has no "degrees of freedom". The desitribution is completely defined by µ and σ², and the standard normal distribution is completely defined by µ=0 and σ²=1. This is not a family of distributions, and there is no dependency on any other parameter (like the degrees of freedom). Could it be that confuse this with the t-distribution?
Not that not the standard deviation but the standard error is multiplied to get the confidence interval.
The solution I gave is answering your question. The quantiles are these factors you are looking for. If you have small samples and if you actually refer to the t-distribution then you need to take the corresponding quantiles of the t-distribution (in Excel: T.INV and T.INV.2S, depending on if wou want a one-sided or two-sided confidence interval; the R-function is qt(.)).
Ah, I see - that's not exactly what I thought it was. These are not confidence limits. I have no idea how the limits given in the tables are calculated :(
Dear Mohd,
You may find these useful:
www.itl.nist.gov/div898/handbook/prc/section2/prc254.htm
www.quantdec.com/envstats/software/intervals.xls
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