Exponential Distribution Tolerance Interval

[#1]

Hello. Having one question, seen the old jump have quantile probability pop-up window feature to type probability to get the quantile number. Not seeing it in JUMP 17 anymore, can I ask if tolerance interval is the same replacing it?   Hoping to find the matching quantile based on the sigma value provided and corresponding probability. i.e. 6 sigma (0.999999999), 4.8 sigma (0.999999)   Selecting one-sided, specifying confidence 0.95 and proportion to cover 0.999999999, can I get the corresponding quantile value?   Thanks in advance  

[#2]

Hello, I am Yusuke Ono, Senior Tester at JMP Japan.

Yes, a one-tailed tolerance interval is acutually the one-tailed confidence interval for the quantile.

You can get the point estimates for quantiles by Quantile Profiler.If you want to calculate a quantile based on an estimated exponential distribution, fit an exponential distribution on the Distribution platform, select
[Profilers] > [Quantile Profiler] at Fitted Exponential Distribution. Type your number (like 0.999999) at the red text at the X-axis. The confidence intervals are not calculated here.

Tolerance intervals are different from point estimates for quantiles. As regards to one-tailed interval, one-taled tolerance intervals are one-tailed confidence intervals for quantiles. For example, one-tailed (95%, 80%) tolerance intervals are 95% confidence intervals for 0.80-th quantile.

In JMP18 (the current JMP version) or before, you can calculate tolerance intervals based on only normal or nonparametric by the Distribution platform. The exponential distribution is not supported. In JMP19 (next JMP version), the Distribution platform will support more probability distributions (like exonential distribution).

You can calculate the approximated one-tailed tolerance intervals by the Life Distribution platform although it uses an approximation. The confindence intervals are calculated here, so you can get, for example, the approximated one-tailed (95%, 80%) tolerance interval based on the exponentail distribution.

You can get the estimated quantile for "0.99999999" or "0.999999" numericaly by the above methods. But it looks very hard to check this extrapolation is reasonable in practice (if sample size is less than about 10000000 or 1000000).