# 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.

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### How does the Empirical Rule align with Tolerance Interval

For Empirical Rule, 95% of the observed data will occur within the second standard deviation, but what is the difference between this and the 95/95 2-sided tolerance interval ? It includes 95% of ...
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### What interval should I use to describe the variation caused by the randomness in stratified random sampling?

I have a population with n individuals. I decide that stratified random sampling is appropriate and I randomly survey a single individual in each strata, ultimately surveying ...
30 views

### Lower confidence with larger sample size? Tolerance interval for distribution-free data

I am trying to find the sample size required in order to establish a tolerance interval which contain 99% of the population, with 95% confidence. The results from Minitab for a sample size of 473 are ...
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### Is it possible to estimate a specific quantile of a prediction based on the results of ordinary linear regression?

We can estimate mean value of a prediction with a specific confidence, we have an estimated value of a variance (MSE) and we also assume that prediction is a normally distributed random variable. Isn'...
19 views

### interval depending on sample size

I came across these funnel plots here and tried to reproduce something similar where I have a normally distributed population and I happen to know the true population mean (500000) and standard ...
28 views

### Tolerance Interval from the posterior predictive distribution of a ratio of two Normal distributions

I am trying to calculate a Beta-Gamma Tolerance Interval from the Posterior Predictive Distribution of a log(ratio) of two normal (no close form available). In the minimal R code below, assume ...
45 views

### tolerance interval, sample size and power

I can only find limited information on how to calculate sample sizes in respect to tolerance intervals. I have a particular problem I would appreciate any help on. If I had a normally distributed ...
218 views

### How to set the tolerance in Gradient descent?

I understand that one solution of setting the number of iterations, is to set it to a large number and then interrupt it when the gradient vector becomes tiny, so tiny that it is smaller than a ...
30 views

### Tolerance Interval of large Time Series data

I have a time series Temperature data coming from a sensor which is collected at a irregular frequency. The data size is ~100K. I have to find the Lower and Upper Bounds for this data to find the ...
56 views

### finding different value while doing regression

My question may sound unclear but I'm going to explain it in detail. I have a data set includes two-column with 50 samples. let's call the first column energy and the second column cracking. Let's ...
169 views

### Confidence intervals for non-parametric statistics

I have a positive random variable $X$ (say, price or latency or energy) and I want to be able to say something like I am 95% confident that $P(X<42)>0.9$ (percentile) or $P(X<22)\ge\frac12$ (...
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### Accounting for unobserved variability in interval estimation

My work involves estimating the strength of materials. Essentially, a manufacturer has samples of a material tested for strength, and then we use that data to compute tolerance intervals. However, ...
17 views

### Confidence Interval For Values

Confidence Intervals help construct a range where you expect the true mean of a population of values to be, given some arbitrary sample. I'm curious if there is an equivalent function you can use, ...
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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 ...
228 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 ...
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### 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 ...
527 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 ...
753 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 ...
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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 ...