# Questions tagged [randomness]

Randomness is the lack of pattern or predictability in events. Randomness is often modeled with probability distributions, but can also be generated by deterministic processes.

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### Precision and recall of a random classifier

My understanding of precision and recall tells me that there is a tradeoff between these two measures: you can improve one at the cost of the other. However, when I think of a random classifier (on a ...
1k views

### How to validate a random sample

I have been given two sets of data, one with 10,000 observations which is a subset of the other with 100,000 observations. It is claimed that the small dataset is a random sample of the large dataset. ...
167 views

### Sanity check to determine if 'random' data on disk drive may have been tampered with

I've got some code that does a Dept of Defense secure erase of disks, and would like to know about a good sanity check to run after the fact. Bottom line, the last write phase of a secure erase of a ...
27 views

### How best to form many short, independent random numbers from one long random number?

I have 20 digit, uniformly distributed random numbers, downloaded from random.org (because the numbers from that source are based on variations in atmospheric pressure rather than a mathematical ...
64 views

### A pseudorandom number generator with a seed greater than 80 bits

I need to generate a sequence of pseudorandom numbers with a period larger than $2^{80}$, using a seed larger than 80 bits, on a 32-bit embedded microprocessor. What are my possible options (in terms ...
128 views

### Relation between statistical randomness, uniform distribution and independence

In Monte Carlo simulation, we often consider how well a sequence of generated points are. If I am correct, one aspect is statistical randomness: A numeric sequence is said to be statistically ...
833 views

### interpreting chi square value for validating random numbers

I am trying to use the chi-square test for identifying random data. I have 256 categories, i.e. 255 degrees of freedom and count the occurrence of byte-values (0-255). As suggested by Knuth, the ...
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### Best way to find non-randomness regions in these or similar count data?

Let say I have data in a shape: [0,0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,2,0,0,0,....] - so mainly zeros.... However I know how long is my 'signal' and how many counts are they. Is it possible ...
42 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 ...
75 views

### Randomized Block Design

It is desired to use a randomized block design with $4$ blocks of size $6$ each for testing the effects of $5$ treatments A,B,C,D and E. In each block, treatments B,C,D and E are replicated once each, ...
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### Clarification on the “tickets in a box interpretation” for random variables

I have a question on the definition of a random variable. I have read the tickets in a box interpretation here and here, which helped me immensely, but I have some doubts for the case in which the ...
67 views

### When random output is a local maximum, how can a neural network find the global (or a better local) maximum?

I'm trying to train a neural network to play Rock-Paper-Scissors. A random player is a local maximum for the game, as it wins 50% of the time. In a tournament setting, it comes out consistently ...
40 views

### Testing for randomness of room assignments

I have data on room assignments for students at a university, as well as certain characteristics on the students in the rooms, e.g. test scores, gpa, nationality, gender. I am told room assignments ...
169 views

### Suggested algorithms for time series analysis of sporadic events

I have a series of sporadic, discrete time series events that appear to occur in shorter interval clusters and I am looking for a way to determine the frequencies at which the events occur. None of ...
65 views

### Auto-Correlation

I had thought that if I call acf() on a vector of integers, and examine the value correlation coefficient at K (lag) = 1, I would expect: A value close to +/-1 would show that the integers are not ...
296 views

### What is the distribution of an outer product of random values mod P?

I haven't been able to answer this daunting question for days now and I am not able to find the right resource for it, so maybe someone here might help me out. Consider an outer product of two ...
87 views

### How to select model when different models are preferred with different seeds?

I am trying to apply the lasso or ridge regression to my data set for the feature selection, but different random seeds produce different models. What is a good or universal way to obtain the final ...
23 views

### Test for random distribution of values in a sequence

I'm looking to measure the degree to which values in a column or list are ordered or pseudo-randomly aligned. In essence I'm trying to distinguish the following scenarios. Say we have a "sex" column ...
37 views

### I am drawing balls of three colours from an urn until it is empty. Is the sequence of colours random?

I have the following problem. I have an urn with n balls of k different colours. I draw balls without replacement until the urn is empty. This leads to a sequence of colours. I now want to show that ...
23 views

### Random sampling at two different frequencies

In a production line, random samples are drawn to be tested for properties A and B. A has to be tested at a higher cadence than B and the assumption is that A and B have zero correlation. Since the ...
40 views

### Is there a known PRNG that passes TestU01's BigCrunch but fails any test in NIST 800-22?

In other words, does TestU01 incorporate all statistical tests by NIST 800-22?
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### purpose of random experiments in Jaynes' Baysian probability theory?

NOTE: I understand the role of random experiments in orthodox probability theory, and its role in providing unbiased estimators and hypothesis tests. Please don't answer this question with basic ...
66 views

### the length of a random walk in two dimensions

This is a matlab code that could generate a random walk in two dimensions of length 1000: xy = cumsum (-1+2*rand(1000,2),1). The 'stepsize' is between $[-1,1]$. In this case, we are talking about ...
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### Comparing the performance of random and weighted-random classifiers

I have a set of 300 observations of known class and there are 20 classes in total. I want to compare the performance of a random classifier with a weighted-random classifier at classifying the ...
324 views

### Uniformity of true random numbers

Are numbers generated by True (hardware) Random Number Generators (TRNGs) more uniform than numbers from a Pseudo Random Number Generator (PRNG)? I understand that there are not much (analytical/...
603 views

### How to do cross validation in Random Forest if the objective is to measure variable importance?

As you know, the random forest algorithm and k-fold cross validation (except the case of Leave One Out) involve randomness. Thus a typical 10-fold CV in one run results in a certain variable ...
23 views

### What's the best method for figuring out whether clusters occurring in data are random or are indicative of an underlying non-random behavior?

I have a dataset of the times that events happen. I noticed some clustering of events but I know that even assuming a random uniform distribution some amount clustering will inevitably occur. How do I ...
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### Detecting extent of randomness of a binary time series

I have several time series that take a value of 1 if an event occurs and 0 otherwise. I would like to measure randomness of each time series is. What would be a good measure for this? The reason I am ...
72 views

### 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 ...
66 views

### How can I test if a string on distinct numbers/characters is random?

Let's say I have a string of 26 letters. I want to permute them and then test if my permutation is random. How do I do this?
280 views

### Calculate probability of random numbers adding up to or being greater than another number

What's a simple formula I can use for calculating the probability of a set of random numbers adding up to or being greater than another number? Where $W$ is the amount of random numbers picked, $X$ is ...
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### Question about word/discourse similarity analysis

Question about a investigative journalistic proof involving LDA and prior along with general probability distribution model for an unusual type of problem. Basically I have an email I wrote to a ...
48 views

### testing randomness in a grid

I need help with figuring out what kind of statistics I need to run to test for randomness in a grid for small mammal trapping. The grid consists on 64 traps, arranged in 8 rows of 8. The image ...
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### A question about random permutations and the probability of their fixed points

I have started off by listing all the random permutations as (1 2 3) (1 3 2) (2 3 1) (2 1 3) (3 2 1) (3 1 2) I have shown that the probability a random permutation has at least one fixed ...
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### Accounting for measurement bias using a histogram or violin plot and numerical data in R

The Problem I have a gardener whose job it is to measure trees in meters using a measuring stick. She measures the heights of 1,000 trees. I plot these measurements on a violin plot in R. I am ...
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### How can I model this problem?

Genetic algorithms are a kind of evolutive approach to problem solving where solutions are randomly generated and crossed with each other as to produce other solutions. With each generation or ...
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### Modeling a list with a tunable degree of disorder/shuffling

Imagine we have a list of ordered numbers $L = (1, 2,\dots, N)$. I want to add an arbitrary amount of "disorder" to that list. For instance: Adding a little bit of disorder would permute a few ...
114 views

### How to test the randomness of a sequence of real m-tuples?

1) Let $\{a_i\}_{i = 1, ...,n}$ be a real sequence generated by a pseudorandom number generator. How can I check the randomness of such real numbers using, for instance, Runs test? 2) Assume three ...
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### Finding a sample to represent a known population

Entire Population: 30,000 Known properties of population: Age, gender, height, weight, Ideal representative sample size: ??? This is for a mailing list test group selection. Problem constraints: ...
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### Ljung-box test on weekly percentage of total quarter bookings

I have a data on the weekly percentage of the total quarter bookings. The data looks as follows (note: weekly percentages add up to 100 for each quarter) : (not real data) I used the Ljung-box test ...
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### 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 ...
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### How to spot/measure artifacts produced by several rotations of 2-dimensional data?

I am trying to transform dataset to mulitiply its size but preserve its initial random nature. I have 5-dimensional numerical dataset which represent particles in plane, produced by Monte Carlo ...