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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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How to do Monte Carlo with conditional input values?

Please apologise my likely ignorance of the correct terminology and notation. Any edits and suggestions to improve the question are very much appreciated. I want to perform a Monte Carlo simulation ...
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4answers
2k views

Check if a character string is not random

Background Let's say we have an alphabet of A,B, C, D, then we look through some data and find a "word" which is DDDDDDDDCDDDDDD ...
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10 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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14 views

Difference between Random Forest and Random Subspaces/Patches

When fitting a Random Forest model, a subset of the features is randomly considered at the splitting of each node. E.g., if $p$ is the number of features, then at each node in each tree, $\sqrt{p}$ ...
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2answers
1k views

What is the state of the art in statistics tests for distinguishing good from bad random number generators?

There are many packages out there. In particular, PractRand gives out an opinion on a number of them, but it's only an opinion. Is there conventional wisdom about which set of set of statistics ...
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1answer
35 views

Why are there different statistics tests in NIST SP 800-90B and NIST SP 800-22? [closed]

NIST SP 800-22 (published in 2010) lists out some statistical tests for telling good random bit generators from bad ones. NIST SP 800-90B (published in 2018) has apparently the same purpose but lists ...
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38 views

How to test if time series data is random

I have many time series data sequences and I would like to produce forecasts for their behaviour in the future. In order to do this I am looking into several methods, but the underlying concept is ...
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0answers
13 views

Sample proportion of 30 independent binary random processes [closed]

Suppose you are interested in π=Probability of Heads for a particular coin. Toss this coin 30 times and record the outcomes in a sequence of H and T’s. Then find the sample proportion of Heads. Find a ...
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2answers
57 views

Why atmospheric noise is considered the only reliable source for generating “pure random numbers”?

When we say that something is random, it simply implies that the occurrence under observation does not have any cause or at least that cause cannot be determined beforehand in layman's language. For a ...
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0answers
25 views

Goodness of fit test for observed samples of binary strings

Consider a process that produces binary strings of varying length $n$. A typical sample would include $n\ $ I Number of strings $1\ $ I $\ 3,000,000$ $2\ $ I $\ 800,000$ $3\ $ I $\ 350,...
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0answers
30 views

why LSTM word based model works better with random input seed than fixed input seed?

I have implemented an LSTM model that have 2 LSTM layers, a dropout layer and a dense layer for predictions. I trained my LSTM model on 1000 XML files. Each file has 4 main markups with very simple ...
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1answer
52 views

Find if a coin toss sequence is random

Suppose we are given a sequence of heads and tails for 1000 coin tosses. how do we check if it's actually random? I believe I need to do a hypothesis test, I tried to write some examples to get an ...
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3answers
111 views

Is it possible to calculate the probability the sum of one set of random variables equals the sum of a different set of random variables?

I'm doing data analysis at the business I work for. 23 people were asked for input for two separate lists. The first list the answers could be any integer 6 to 10. The second list the answers could be ...
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1answer
69 views

NIST Randomness Test, Testu01, Dieharder

the NIST Randomness Test, Testu01, Dieharder all seem to offer a suite of tests to check psuedo random number generators(PRNG) for randomness. I was hoping someone with experience of those tools could ...
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0answers
16 views

How to properly cross validate a model that is affected by randomness in the training procedure?

Many machine learning models are affected by some amount of randomness as part of their training procedure. For example the performance of a neural network model can be highly affected by the initial ...
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1answer
22 views

Hypothesis testing with randomised algorithm

Imagine I have some data D, and with a randomised algorithm I construct a parameter $\theta$. I know the distribution of $\theta$ under the null hypothesis of the data. For example, the original data ...
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2answers
69 views

Dataset partitioning issue of cross-validation

Every time the cross-validation is run, the dataset is partitioned into k even groups randomly. That means every time the result of cross-validation can be different, so which one should we take to ...
2
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1answer
267 views

Confused about how to interpret Chi square results

For my local charity I have to organize random draws, each week to give a prize. I just bought a random machine generator, which randomly spits one ball out of 10. Before using the machine in public ...
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0answers
23 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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1answer
17 views

Within individual independence testing

I have a group of individuals that is independent and identical distributed. Within each individual $i$, one may observe $N_i$ observations. The task is to test whether the within-individual ...
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3answers
749 views

Why do several (if not all) parametric hypothesis tests assume random sampling?

Tests like Z, t, and several others assume that the data is based on a random sampling. Why? Suppose that I'm doing experimental research, where I care much more for the internal validity than the ...
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1answer
470 views

Is PCG random number generator as good as claimed?

I have a demand for extremely fast acceptable-quality random number generator (RNG). This means rand()%2 should not alternate between 0 and 1 (that totally kills the simulation, as in one problem I ...
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1answer
98 views

How to generate randomness using a biased coin? [closed]

Imagine we have three people and we want to select one of them at random. If we had a fair coin we could have tossed the coin twice to get one of the 4 outcomes and could have related the occurrence ...
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50 views

Randomly split batches for time series CV

In certain code snippets for time series prediction, I find sometimes that authors split their data to train and test sets (nothing unusual for the moment). But then the train data is split into ...
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0answers
76 views

Generate sequence of random autocorrelated numbers

Back in the university I was working on a program that generates a sequence of random autocorrelated numbers. Autocorrelated meaning that each next value is close to the previous one and depends on it ...
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1answer
41 views

Random sampling a matrix to reflect a real world case

I'm trying to create two matrices one that can be filled with 0's and 0.25's and another with 0's and 1's. ...
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0answers
49 views

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 ...
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2answers
85 views

But what is a random experiment

I am currently thinking a lot about the definition of probability and one thing that I am really not content with at all is the frequentist definition of probability as long run relative frequencies ...
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0answers
17 views

Random distribution exercise

I have the following problem to solve and I don't know when to start. Please see example below to get an idea of it. There is 5 persons (A, B, C, D, E) that need to be fed with apples for 10 days. ...
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23 views

Random sequence and uniform distribution? Is this always the case?

(Short version) Is this always the case that a truly generated random sequence (of whole numbers) conforms to (or at least expected to conform to) a uniform distribution? (Long version) The most ...
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0answers
28 views

Algo to identify next numbers in a row that looks random (but isn't) [duplicate]

I was wondering what would be your approach on building an algorithm that needs to guess the next numbers based on a given row of numbers, that seem random but maybe follow some rule - the algo is ...
3
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0answers
22 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 ...
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0answers
17 views

Statistical tests for PRNG that generates a sequence which is not binary

I have already asked this question on crypto.stackexchange but I think here is the appropraite site for this. Is there a pratical application to PRNG that generates a sequence which is not a binary ...
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1answer
158 views

Establishing the Probability Distribution that Governs a Random Process

I have a experiment in which a random event that can occur $N$ times in some set period of time $T$ (where $N \in$ $\mathbb{N_0}$ but is typically less that 10 and never exceeds 100). Here I will ...
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76 views

Using Kalman Filter to estimate parameters in a CIR process

I am trying to estimate the parameters in a system $ds(t) = r$ $dr(t) = \beta(\alpha-r)dt + \sigma \sqrt{r}dW$ where $W$ follows a Wiener process, so $r$ follows a ...
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4answers
58 views

Probability and randomness

Assume that we toss a coin n times and the result looks like this HTHTHTHTHTHTHTHT... . Would a (Probability-) Frequentist conclude that that the probability for the coin to land heads is 0.5? It ...
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1answer
48 views

In Deep Learning, how much does randomness help generalization?

Let's assume at the beginning the NN is initialized with random weights, then the Backpropagation "shapes" the weights but the signal is strongest close to the final layer (where it gets computed) and ...
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2answers
698 views

Will this introduce bias into what should be random numbers?

Assume a data file with 80+ million ones and zeros, randomly generated. From this file, we want to create a list of random decimal integers. This is the plan to do this conversion. Divide the 80 ...
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1answer
15 views

Unsupervised learning problem: rate individual survey submissions on randomness of data entered

For my work we collect a lot of surveys which contain a mix of questions: multiple choice, checkbox and numeric. We know that in some instances enumerators might fudge the survey by entering answers ...
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1answer
54 views

Why does the law of large number hold for pseudorandom numbers

i`m wondering why the law of large numbers holds for pseudorandom numbers. Is this a empirical observation such as that the law of large numbers holds for coin tosses, or is this somehow programmed ...
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61 views

Simulating from the Gaussian Distribution

I attempted to sample random variables from the Gaussian distribution in C using the following simulation method: $$X_n = \sqrt{(-2\log(U_1)}\cos{(2\pi U_2)}$$ Where $U_1, U_2 \sim \mathcal{U}(0,\,...
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0answers
38 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 ...
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1answer
29 views

Is there any way to derive the initial accuracy with random initialization?

In many iterative machine learning algorithms, weight/parameters are initialized as random. But is there any mathematical relationship between the random starting point and initial accuracy? For ...
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1answer
357 views

Testing for a Poisson process

Q1. I want to test if my data are the result of a Poisson process. I need to check if: (1) The number of arrivals N(t) in a subinterval of length t obeys the Poisson(λt) distribution or (2) The inter-...
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110 views

Random numbers without pre-specified distribution (revised)

I am trying to simulate the diet of the participants of an observational cohort (say n=10,000 - but could be larger). The purpose is two-fold: first I would like to use this to test some scripts, but ...
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9 views

Would a uniform random distribution (a fair die) produce these results? [duplicate]

I rolled a virtual die 126003 times, with the following results: 1 - 21162 times 2 - 20986 times 3 - 21131 times 4 - 21049 times 5 - 20940 times 6 - 20735 times Does this seem like the right amount ...
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1answer
110 views

What is the probability that a coin is a loaded coin?

If you randomly pick a coin from a box that contains $90\%$ fair coins and $10\%$ loaded coins, (a loaded coin gives heads $90\%$ of the time), toss it $5$ times and get all heads. What is the ...
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31 views

What is wrong with this self-made array shuffling algorithm? [duplicate]

I'm aware of the established array-shuffling algorithms, such as Knuth-Fisher-Yates. I'm interested in proving (or disproving) that my self-made shuffling algorithm is broken. It seems to be the ...
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1answer
65 views

Occurrence of at least 1 HT and HH in sequences of 4 coin flips not equally likely

I was reading this interesting article on hot hands and streaks in sports. The article revolves around the 16 possible sequences of 4 coin flips (H = heads, T = tails): ...
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1answer
33 views

Probability of homework being graded?

Say you have a class with 15 assignments. Over the course of the semester the teacher randomly choses 5 assignments to grade. The teacher also wants to keep it a surprise, that means the first ...