Questions tagged [runs]

Runs refers to repeated occurrences of one outcome. For example, in repeated tosses of a coin, there will be runs of heads and tails. In the sequence HHHTHT there are 4 runs (one of length 3 and 3 of length 1).

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Is it normal to get more variance in k folds cross-validation of an algorithm than in k repetitions?

Is it normal to get a lot more variance in k folds cross-validation of an algorithm than in k repetitions of the same algorithm (neural network) on the same dataset? ...
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Deriving the average and variance of number of runs in runs test

NIST states that the average and variance of a number of runs in the "runs above and below median" test as $$ \overline{R} = \frac{2n_a n_b}{n_a + n_b} + 1 \\ s^2 = \frac{2n_a n_b(2n_a n_b - n_a - n_b)...
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How can I use the distribution of run lengths to test if a sequence is generated from flips of a fair coin?

I have a very long sequence (in the tens of thousands) of binary outcomes from some data-generating process. I believe that these outcomes are iid Bernoulli trials with p = 0.5, equivalent to flipping ...
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39 views

Including streaks/runs in (generalized) linear mixed model context

The data and model used so far: I have longitudinal count data on 16 pens (8 with treatment A, 8 with treatment B). Each pen houses the same number of animals, and the pens may be considered as ...
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Expected number of wins until $k$ consecutive wins

We play the game, where probability that you win a game is $p$. You play until you win $k$ consecutive games. What is expected number of games you win? I can compute that expected number of games is $\...
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192 views

Probability of Runs

I hope the title accurately reflects my question. I have an independent event, with a 98% chance of occurring. Now, I observe and record the outcome of this event 100 times. What is the probability ...
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385 views

Runs test and Durbin-Watson test yield different outcomes

I have analysed the market return using the runs test and the Durbin-Watson test to determine whether the return series follow the random walk or not. The problem I have found is that some return ...
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UP/DOWN Run test: How to determine the Matrix $A$

A test statistic for a UP/DOWN run is defined in Donald E. Knuth, The Art of Computer Programming Volume 2, 1998, pp. 66-.: $V= \frac{1}{n} \sum_{i,j\ <=m} \ (COUNT(i)-nb_i)(COUNT(j)-b_j)a_{ij}$ ...
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Taking two sets (A, B) out of the same distribution, merging and then sorting should roughly result in a,b,a,b,a,b?

Suppose I take 2 sets ($A$ and $B$) of 1000 random items out the same distribution; I also suppose that all items are different. I then create a new set $C$ which is the union of $A$ and $B$, since ...
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586 views

Estimating number of Monte Carlo runs to evaluate a percentile

I have a complex distribution which I can numerically sample. I'd like to estimate a percentile (let's say 90%) using Monte-Carlo simulations. What I'm doing is: I run 1 million of independent ...
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Variation of Wald–Wolfowitz detecting seasonal patterns?

I am considering the standard test for randomness based on runs(Wald–Wolfowitz runs test). In it, you basically take a sequence of 1's and 2's, having length $n$, $n_1$ 1's, $n_2$ 2's and you want to ...
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CLT and Wald-Wolfowitz runs test asymptotic distribution

I need help finding a theorem which could be used to prove that the Wald-Wolfowitz runs test is asymptotically normal. Let me formalize my question. We have a random sample $\{X_0,X_1,...,X_n\}$ (if ...
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run test with p-value equals to NA

I am using runs.test() of library lawstat in R. I am getting following output ...
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375 views

Runs test for a very small sample

I have six measurements taken at different time-points in an experiment, and I want to show if these measurements have a dependence on time (i.e. are they random or not). I originally presented the ...
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Runs of the same type within a deck of cards - distribution of runs of different length

My background is in physics, not statistics, so forgive any suspect terminology or notation, but I hope the problem is clearly set out below. Secondly, my statistics is not good enough to recognize ...
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372 views

One sample run test, but with P(+) $\neq \frac{_1}{^2}$

I am trying to find out how to conduct run tests on one sample but with a non 0.5-0.5 underlying occurrence pattern of the two dichotomous values. For instance ...
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82 views

Distribution of (maximum) run length

I am curious about the distribution of (maximum) run length given k independent trials when $p(X=1)=p_1, p(X=2)=p_2, ..., p(X=n)=p_n.$ For example, for a coin tossing for 3 independent trials, $p(...
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Upper and lower limits for numbers of runs

On this website about statistical process control there is a chart which gives the upper and lower limits for the number of runs in a set of data for the data set to be considered taken from a process ...
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247 views

Runs test for randomness for k elements

Say I have a sequence of length $n$ of $k$ different elements, s.t. $n > k, k > 2$. I want to show this sequence is random, based on the number of runs. I found this paper by AM Mood which ...
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679 views

Null hypothesis of the Wald-Wolfowitz runs test

From Wikipedia The runs test (also called Wald–Wolfowitz test after Abraham Wald and Jacob Wolfowitz) is a non-parametric statistical test that checks a randomness hypothesis for a two-valued data ...