# 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).

31 questions
Filter by
Sorted by
Tagged with
1 vote
33 views

### R function to calculate number of runs in a sequence of numbers [migrated]

I have this sequence of numbers, ...
21 views

### Expected number of runs when there are $n_1$ objects of one kind and $n_2$ objects of second kind. Flaw in Argument?

Suppose there are $n_1$ objects of one kind and $n_2$ objects of the second kind. These objects appear randomly in a sequence. I want to find the expected number of runs in the sequence. Attempt: ...
21 views

### Statistics on an event happening in a series of records

I'm at a loss to calculate the theoretical probability of an event happening. I'll appreciate any kind of guidance. Say i have a few thousand records with a simple series of -1 or 1 with something ...
48 views

### Joint distribution of longest run and number of runs in a sequence of $n$ coin tosses?

A coin with probability of heads $p \in (0, 1)$ is tossed $n$ times. What is the joint probability distribution of the number of runs and the longest run? Schilling (1990) discusses the distribution ...
1 vote
16 views

### LR test for overlapping return data using bootstrap

I wish to test a null hypothesis as in Christoffersen (1998) to see whether a sequence of Value-at-Risk forecasts $Q_t(p) \in \mathcal{F}_t$ possesses correct conditional coverage. Here $p \in [0,1]$ ...
1 vote
21 views

### How to run test for randomness on a ternary cyclic sequence?

I would like to do a run test for randomness on a ternary sequence ($x_n \in \{0,1,2\}$) where a run is said to continue if the value increases by 1 cyclically (i.e. $(x_{n+1}-x_n)=1 \text{ mod } 3$). ...
38 views

### Probability of n successful runs [duplicate]

My background the past while has been project management so I haven't really had much work with stats the past decade or so, so please forgive the terminology if it is wrong. I'm working on a problem ...
13 views

### What are the necessary steps required for conducting a Wolfowitz runs test of randomness, given that I have all the necessary data?

I am writing a part in my thesis about the random-walk theory of price changes. I plan to set up a runs test of randomness to show whether the price changes do follow a particular random pattern. I ...
1 vote
239 views

### 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? ...
119 views

### 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)...
70 views

### maximum randomness and non-randomness

Two questions about randomness of data-sequences: Using a variant of run test like Wald–Wolfowitz to check randomness hypothesis for a one-sample data sequence, which yields a P value denoting the ...
1 vote
63 views

### 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 ...
1 vote
57 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 ...
584 views

1 vote
58 views

### 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 ...
312 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 ...
1 vote
1k 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 ...