Questions tagged [binomial-distribution]

The binomial distribution gives the frequencies of "successes" in a fixed number of independent "trials". Use this tag for questions about data that might be binomially distributed or for questions about the theory of this distribution.

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Consecutive coin flips, what is the appropriate statistical test for this word problem? [closed]

I was listening to a podcast by NDGT (Neil deGrasse Tyson, a prominent scientist) and he posed a simple thought experiment to illustrate the susceptibilities to cognitive bias. What I've come here to ...
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Computing sample size for a sample to estimate binomial distribution when point estimate of proportion is 0

For example, I have a estimate of p = 0 (95% CI: 0, 0.01), and I want to know the sample size for this sample. For $p\not =0$, I can compute the s.e. by $\sqrt(p(1-p)/n)$ to get the $n$, but not sure ...
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Number of confidence intervals for Binomial Distribution

Consider the random variable $X$ to denote the event that the confidence interval cover the unknown parameter or not. Thus, X will follow the Bernoulli distribution with a parameter $θ$, i.e. $X~Be(θ)$...
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Bounds on the conditional variance of a truncated binomial

I have a binomial variable $R$ drawn from $binom(N, p)$, and I'm interested in the variance of $R$, given $R \ge Q$. The pmf of this variable $R^*$ is $$\phi_{R^*}(l) = \frac{\phi(l, N, p)}{P}$$ ...
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Testing sequence of ones and zeros for randomness

I am given a sequence of $40$ ones and zeros and I have to test the null hypothesis that ${40 \choose n_1}$ sequences are all equally probable ($n_1$ being the number of ones). To do so, I have to use ...
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How to deal with ragged power curve

I am exploring various methods for sample size calculation and power analysis from binomial data, and frequently coming up against ragged power curves that go up and down as sample size increases. I ...
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Coeficients from binomial probit model with more than one predictor

A bird observed at time t will have started moult when its time of onset is before t. This occurs with probability given by Prob (started moult before time t) = Φ[(t − μ)/σ], where the function Φ ...
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How to estimate upper CI of population prevalence of (very) rare events - with weights

I'm doing something equivalent to estimating the prevalence of a rare disease. I might sample 1000 individuals, and find zero cases. In which case I'd calculate the upper confidence interval using ...
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Is there a test (in R) for predicting the proportion of "successes" to "failures"?

As I understand it, binomial logistic regression is good for predicting the probability of a "1" outcome from a discrete binomial distribution. What if instead, one wanted to predict the ...
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