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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Overdispersion in a binomial GLMER model

I'm having trouble accounting for overdispersion in a binomial GLMER (lme4 package) - I'd read through other posts on the topic but haven't found anything that solves my problem. I tried adding an ...
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I'm struggling with a contradiction when trying to determine a sample size when proportion is small. If I use binomial formula: $n = p(1-p)z^2/ME^2$ then the smaller the proportion - the smaller ...
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Hierarchical model: question on frequentist estimation

I am interested in understanding the differences between Bayesian and Frequentist estimation in the context of hierarchical models. Consider $n$ subjects, where for subject $i$ there are $k_i$ ...
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Interaction plot between categorical and quadratic continuous variable

I ran a GLMM model with a binomial response to analyse bear presence at feeding sites (0 = absent, 1 = present) within two years. My code is: ...
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Detecting outliers in percentages

My dataset looks like below - Total Success Percentage 100 65 65% 50 25 50% 30 20 66.6% 50 40 80% Plot - Each row is ...
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Including seasons and months into GLMM: should they be crossed or nested effects?

I have collected data from five consecutive fishing seasons (five factor levels). Each fishing season has five months within (five factor levels). Considering that I have a temporal correlation in my ...
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Linear mixed effect model with fractional/proportional outcome: choosing between binomial and beta

I'm looking to run a linear mixed effect model using lme4, where my dependent variable one_syllable_words / total_words_generated is a proportion and my random ...
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Use Chi-Squared or Binomial Test if Distribution is not Known?

Suppose you have a set of data (eg. [a, b, a, a, b, b, etc.]), and you have the suspicion that the set of data follows the binomial distribution. Your Null Hypothesis is: The probability of success ...
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Hypothesis testing for binomial distribution: a simple real-life case

I'm refreshing (or maybe just acquiring) some stats skills, and I have a real-life situation, probably very simple since it's quite close to a typical example from stats courses, that I would like to ...
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The marginals of a truncated multinomial are truncated binomials?

The multinomial distribution for a vector $\vec x$ of non-negative integers assigns a probability of: $$f(\vec x) = n!\prod_i p_i^{x_i}/x_i!$$ to every vector $\vec x$ of non-negative integers in ...
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Put constraint on max (or min) predicted value (mgcv)

I want to fit my data using a logistic GAM model with cubic regression splines. I know for sure that in reality my estimated probability should not go above 0.5 (due to mislabeling). So I thought ...
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Theoretical justification of choice for confidence interval exact method for the success probability parameter of negative binomial variable?

I have a computer experiment that runs the Bernoulli series with unknown probability $p$ of success. The experiment terminates when $m$ failures are observed. So, the unknown parameter $p$ has the ...
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Simple $\chi^2$ test question

I have the following question which seems extremely easy, but the way the data are set up is causing me some uncertainty: I plan to solve this problem through finding the maximum likelihood estimate ...
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sampling order sum from different order size and probabilities

I want to analyze the probable outcomes of an order pipeline for a business. Say we have ten potential orders, each (business) order has a different size (OS), say 1, 20, 3, 4, 5, 6, 6, 8, 8, 9 (mio) ...
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Differences from logistic regression and mixed effects logistic regression - rounding error or conceptual mistake?

I'm a bit confused. To my understanding, the standard logistic regression should be equivalent to a mixed effect logistic regression where the statistical unit is defined as random effect - but I ...
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Residuals in Negative Binomial Data

I'm tackling the problem of Anomaly Detection in a dataset that's comprised of call counts to a call-centre. The data exhibits daily and weekly seasonality and is known to be over-dispersed. ...
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