All Questions
Tagged with estimators confidence-interval
22
questions
5
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3
answers
682
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confidence intervals for proportions containing a theoretically impossible value (zero)
This is really a hypothetical question not related to an actual issue I have, so this question is just out of curiosity. I'm aware of this other related question What should I do when a confidence ...
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4
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1
answer
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Confidence interval on ratio of estimates for exponential random variables
Given exponential random variable X, the MLE for the scale parameter is $\hat{\beta_x} = \bar{x}$, and the confidence interval for that estimate is:
$$\frac{2n\bar{x}}{\chi^2_{\frac{\alpha}{2},2n}} &...
- 1,162
1
vote
1
answer
41
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Combining two success runs in parallel
The goal is to calculate the reliability of a process. Here reliability is defined as follows:
Definitions and tests I used
Let $X$ be a random variable that is equal to $1$ when no defect is present ...
- 472
0
votes
1
answer
539
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Maximum-likelihood estimator for data points with errors
Suppose there are N measurements of a random variable x which has Gaussian p.d.f. with unknown mean $\mu$ and variance $\sigma^2$. Classical textbook solution for estimation $\mu$ and $\sigma$ is to ...
3
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0
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39
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Adjusting confidence interval of estimator by efficiency
Summary: If we have an unbiased MLE $\widehat{\sigma_1}$ of an exponential distribution parameter, and the confidence intervals for its estimates are given by the $\chi^2$ distribution; and we find ...
- 1,162
0
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0
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38
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Confusing usage of Central Limit Theorem
The CLT defined in Introduction to Mathematical Statistics (Hogg) 8th ed., states that given the samples $\mathbf X\sim\mathcal N(\mu,\sigma) $ with the mean and variance estimator $\bar X,S^2$, the ...
- 777
1
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0
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163
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Confidence Intervals for Normalized Random Variables
I think I have a pretty simple question about constructing confidence intervals for normalized random variables.
If I have i.i.d random variables $X_1, X_2, X_3, ..., X_n \sim F$ for some distribution ...
- 111
1
vote
0
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47
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Correct approach for combining confidence intervals from multiple estimators
Let's say I have an estimation from 2 different people about human population of a small town. Both are (calibrated) 90% CIs:
Expert 1: 3,000-4,000
Expert 2: 3,000-50,000 (Intentionally much wider ...
- 11
0
votes
1
answer
312
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Do confidence intervals make sense for win rates in sport?
Imagine we have 2 teams play 10 matches against each other with team A winning 6 of them I.e. 60%. In this setting do confidence intervals for the probability of winning make sense? On one hand I ...
- 810
1
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0
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128
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Confidence interval for exponentially distributed estimator
We have an estimator $\hat{\theta}\geq 0$ for $\theta$, with distribution function $P\{\hat{\theta}\leq t \}=1-e^{-t/\theta}$, which we can recognize as the cdf of the exponential distribution. Our ...
- 85
0
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0
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88
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Replace parameter with estimate for confidence interval. Case Beta distribution
I'm trying to get a confidence interval for the mean of a beta distribution $B(\theta,1)$, using $[\hat\theta - z_{1-\alpha/2}\hat\sigma_{\hat\theta};\hat\theta + z_{1-\alpha/2}\hat\sigma_{\hat\theta}]...
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13
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3
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Revisiting the Rule of Three
The rule of three is a method for calculating a 95% confidence interval when estimating $p$ from a set of $n$ IID Bernoulli trials with no successes.
My understanding from its derivation is that the ...
- 1,463
0
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1
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4k
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What's the advantage of a point estimate over an interval estimate?
A point estimate is :
A single numerical value that is used to estimate the corresponding population parameter.
Whereas an interval estimate is :
An estimate that consists of two numerical values ...
- 37
0
votes
0
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24
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How to estimate differences between two normal means when variances are tested to be unequal
Let $X_1 X_2...X_n, Y_1 Y_2...Y_n$ be $\sim N(\mu_x$, $\sigma_x^2$), $\sim N(\mu_y, \sigma_y^2$).
I want to estimate ($\mu_x - \mu_y$) and have used F-test to see that $\sigma_x^2$ $\neq$ $\sigma_y^2$ ...
- 215
1
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0
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How to estimate the confidence interval for a "predicted difference" from a quadratic model?
Assume you have past consumption levels $c_1, \dots c_n$ at times $t_1, \dots t_n$ and cumulated consumption levels $y_1=c_1, y_2 = c_1 + c_2, \dots y_n=\sum_{k=1}^{n} c_k$.
(I use the quadratic term ...
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