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4
votes
1answer
97 views

Joint pdf of functions of order statistics

Let $ Y_1 < Y_2 <\ldots <Y_{10}$ be the order statistics of a random sample from a continuous type distribution with cdf $F(x)$. How would I begin to show that the joint distribution of ...
5
votes
2answers
293 views

Normality Testing - Choose the transformation that makes the data “most normal”?

Background: I have conducted some testing on a random sample of n=20 parts. The data is variable and I know nothing about the population statistics. I would like to use the data from this sample to ...
3
votes
1answer
101 views

Decision rule using tolerance intervals

I'm testing a new instrument with the traditional instrument and taking measurements on the same subject using both instruments. I want to be able to make a statement that "at least 95% of the ...
2
votes
1answer
103 views

One sided dist-free tolerance intervals and testing

I am involved in writing a standard where test labs are trying to decide sample sizes for a new device. The suggestion has been that using ISO 16269-6: Table F.1 ("sample size for a proportion p at ...
-1
votes
1answer
508 views

Some clear range and interval definitions

What is your or an offical (please provide link to citation) definition of range AND interval _? Or perhaps put in another way: what is the major important difference between the two terms _? My ...
7
votes
2answers
316 views

Tolerance bound for a normalized variable

Based on a sample $(x_i) \sim_{\text{iid}} {\cal N}(\mu, \sigma^2)$, how can you get an exact or a well-approximated upper tolerance bound (i.e. an upper confidence bound of a quantile of the ...
3
votes
1answer
224 views

Tolerance interval for Deming regression

I am trying to derive (one-sided) tolerance intervals related to the Deming regression model: $$ x_i=x^*_i + \epsilon_i$$ $$ y_i = (\alpha+\beta x^*_i) + \epsilon'_i$$ where the $x^*_i$'s are ...
4
votes
1answer
343 views

What is the equivalent of a standard deviation when considering a least squares fit line?

I am calculating a tolerance interval following http://www.itl.nist.gov/div898/handbook/prc/section2/prc253.htm but this says to multiply the k value by the standard deviation of the sample. I have a ...
4
votes
1answer
830 views

Prediction and Tolerance Intervals

I have a couple of questions for prediction and tolerance intervals. Let's agree on the definition of the tolerance intervals first: We are given a confidence level, say 90%, the percentage of the ...
1
vote
1answer
290 views

Prediction vs. tolerance interval

I want to predict a factor and also get an upper bound for my prediction. It seems that what I want is prediction interval. but prediction interval only specifies the bound for one next prediction not ...