# Questions tagged [coverage-probability]

The probability that a confidence interval actually contains the true parameter.

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### Convergence of Sum of Sums of random variables : trivial?

I have a sequence of i.i.d random varaibles $X_1, X_2, ...$ with finite mean $\mu$ and finite variance. I also have another sequence of i.i.d random varaibles $Y_1, Y_2, ...$ with the same finite mean ...
149 views

### Coverage probability from fiducial/confidence distribution

I am trying to realize how to compute confidence intervals from a fiducial distribution/confidence distribution with possibly more than one parameter. But for now I would just like to understand if I ...
84 views

### Probability distribution of three random variables

The following formula is a formula I got from a paper that deals with wireless networks specifically when calculating coverage probabilities, it is powerful because one can use it for general ...
593 views

### Calculating the mean excess loss

Suppose $X$ has the following pdf: $$f_x(x)=0.01 \qquad for\space 0\le x<100$$ Find the pdf of $X_p$ (the excess-loss variable) and calculate the mean excess loss for $d=10$. \begin{align} P(X_p&...
73 views

### error on truncated rms

I am computing the RMS of a sample to estimate the standar error $\sigma$ of the underlying distribution (for simplicity let say a normal distribution $N[\mu$, $\sigma$]). \$ \text{RMS} = \sum_{i=1}^N ...
168 views

### Why (mathematically) is the parametric bootstrap usually better than the empirical one?

As I know from experience, the parametric bootstrap performs better in terms of coverage probability for confidence intervals then the empirical bootstrap. Of course, this makes sense because you put ...
289 views

### Inconsistency between RMSE and 95% CI Coverage

I am running simulations to compare different weighting methods to estimate the mean of y (with missing values). I use bias, RMSE and 95% CI Coverage as my performance metrics. However, looking at ...
459 views

### Confidence Interval Coverage-error and Type I error

Could somebody explain to me the relationship between coverage error and type one errors in multiple comparisons testing, if there is one in fact? Does a coverage error occur when the true value of ...
369 views

### Why are intervals for means narrower than intervals for individual observations?

I am looking at problem 5.01 relating to Galton's data on adult heights of fathers and sons, from Chapter 5 of Statistical Modelling: A Fresh Approach link to this book: http://www.mosaic-web.org/go/...