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Questions tagged [tolerance-interval]

A tolerance interval is an interval that contains $p\%$ of a population with $(1-\alpha)$ confidence. A TI is distinct from (but sometimes confused with) prediction intervals & confidence intervals.

A Tolerance Interval (TI) is an interval that contains $p\%$ of a population with $(1-\alpha)$ confidence. A tolerance interval can be contrasted with a prediction interval that has a $p\%$ probability of containing a future value (realization) drawn from the population, and a confidence interval that contains the true value of a parameter (e.g., the mean) with $(1-\alpha)$ confidence. Note that a tolerance interval is specified by two values (the desired proportion, and the desired confidence), whereas prediction intervals and confidence intervals are specified by only one.

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How to obtain a confidence interval for a percentile?

I have a bunch of raw data values that are dollar amounts and I want to find a confidence interval for a percentile of that data. Is there a formula for such a confidence interval?
GeoffDS
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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 population to capture, say 99%, and a sample size,…
Ioannis Souldatos
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Nonparametric tolerance intervals for discrete variables

Suppose you have a bunch of people rate how much they liked a movie on a discrete scale from 1 to 10, and you would like an interval [l, u] such that with (at least) 95% confidence, (at least) 90% of all people who see the movie will rate it no…
Kodiologist
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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 distribution) of $\dfrac{x_i}{\sigma}$ ? Here, we assume…
Stéphane Laurent
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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 model with a fit line, so I would think I do not…
Aerik
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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 nonrandom fixed numbers, $\epsilon_i \sim {\cal…
Stéphane Laurent
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How do I know whether future samples will remain below a threshold?

I have N samples of quantity x (N=40 or 50 or so; I illustrate 7 of them here). 0.529578449 0.24137483 0.715602119 0.541831981 0.426401788 0.426117433 0.678243369 .... To these I can reasonably fit e.g. a normal distribution with, say, mean 0.51…
Jean-François Corbett
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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 make statements about the population (in…
user31189
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Joint pdf of functions of order statistics

Let $ Y_1 < Y_2 <\ldots
JohnK
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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 differences between the two is no more than 0.05 units".…
stats134711
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Making a forecast: Confidence/Prediction/Tolerance Interval?

I understand the the difference between these three types of intervals but I will summarize briefly: Confidence Interval: an interval that will contain the true mean value say, 95%, of the time. Prediction Interval: an interval that will contain…
a.powell
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Conditioning within definition explanation

I have a doubt on the meaning of a conditioning within a definition. In a book I've found the following definition of upper tolerance limit: $P(P(X<\bar X+kS|\bar X, S)>p)=1-\alpha$ where $X$ is a random variable, $\bar X$ is the sample mean of…
xanz
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One Sigma error and 68% tolerance interval

I have first a clarifying question, and second, a question asking about how to do something, depending on the answer to the first question. Suppose you have a set of data of some PDF which is non-gaussian. The standard equation for the sample…
zephyr
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Creating a tolerance range for measuring performance

Apologies for my ignorance, I've been trying to find an answer to my question but I think my understanding of statistical analysis is so rudimentary it has been confusing. I want to use a statistical method to determine what is an acceptable range…
Open Boxes
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Tolerance interval for Poisson

I am an R user and need to figure out how to compute a tolerance interval for a Poisson distribution with lambda = 120. I would like to get a 1-sided upper tolerance interval with alpha = 0.05 and proportion = 0.99.
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