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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Why not use always a binomial exact test to compare two proportions instead of chi square?

I am trying to figure out what test I should use in the following scenario: I know that there is a lot of room for improvement in a specific area at work - being extremely critical, let's say that ...
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25 views

Laplace approximation for binomial distribution in matlab

i using bionrnd() function to generate a random vector and Laplace approximation formula to approximate the binomial distribution. but Laplace histogram dose not ...
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47 views

Is there a way to do a statistical test if an independent variable has only 1 level?

I have a repeated measures design in which I tested multiple individuals with three different sounds (playbacks). The playbacks were 20 seconds in length and I recorded 1) how individuals responded ...
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1answer
22 views

Assessing fit of binomial glmer() in R with only categorical predictors

I am trying to validate a mixed effects logit regression model with a categorical dependent variable and categorical predictor variables - I have nothing that is continuous. One of my predictor ...
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1answer
21 views

Developing probability distributions

An event occurs, and after this event has occurred there is a set of conclusions which can be drawn. All of these conclusions have results which are distinct. I am trying to keep this as general as ...
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1answer
45 views

Difficulty with power analysis

I need to estimate sample size for an experiment but I am not very knowledgeable about power analysis. In my experiment, I am asking if a user can notice the two possible states of a system. I ...
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0answers
24 views

Uniformly Most Poweful Hypothesis test for the difference between two means

I have data for two groups, $G_1$ of n trials and $G_2$ of m trials, of which datasets $x_1$ and $x_2$ have been collected. These can be binomially distributed, $X_1$ ~ B(n,p), $X_2$ ~ B(m,q). I ...
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How to tell the probability of failure if there were no failures?

I was wondering if there is a way to tell the probability of something failing (a product) if we have 100,000 products in the field for 1 year and with no failures? What is the probability that one of ...
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13 views

What is the best approach to measuring significance in two binomial distributions?

I have been using the Wilson score interval to determine whether the registration rate from two different website flows are significantly different. I want to see if there are suggestions for better ...
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64 views

Asymptotic distribution of the max (min) of IID binomial variables

I would like to know the limiting distribution when $k \uparrow \infty$ and $k/n \rightarrow \lambda$ of $$ \max(X_1, \ldots, X_k), \text{ where $X_i$ are IID $B(n,p)$}.$$ This is most likely a ...
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1answer
12 views

Bit Error Rate - Multiple Bernoulli trials with different probabilities

If you transmit a sequence of bits over some line, errors may creep in. For instance, if the Bit Error Rate of this line is 1%, on average, every 1 out of 100 bits will flip to the opposite value. ...
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1answer
32 views

How to calculate probability that another player has a card

In a poker game, how would we calculate the probability that another player has at least one certain card? Lets say that there are five other player, there are four cards in middle of the table, and ...
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1answer
53 views

Chi-square test p-value = 1

I am attempting to use the chi-square test as a goodness-of-fitness test in R, but I keep getting a p-value = 1. I expect a high p-value, but less than one. Can anyone point out what error I might be ...
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1answer
49 views

Hypothesis Testing for survey

Suppose my null hypothesis is “Not more than 50% person prefer milk” and alternate hypothesis is “More than 50% (or majority) prefer milk”. Actually the null and alternate hypothesis are set so only ...
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1answer
112 views

Overdispersion and Underdispersion in Negative Binomial/Poisson Regression

I was performing a Poisson regression in SAS and found that the Pearson chi-squared value divided by the degrees of freedom was around 5, indicating significant overdispersion. So, I fit a negative ...
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0answers
14 views

Probit regression with misclassified binary dependent variable in R

Is there a generalized linear mixed-effects model implementation for R that could handle misclassified binary data? Unless I have overlooked something in the documentation, glmer with ...
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2answers
52 views

When is calculating probability based on a poisson distribution preferred over a binomial distribution?

I'm trying to understand why a poisson distribution may be preferred over a binomial one when modeling binary cases. Is there a case where you can't use a binomial distribution to solve a problem ...
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1answer
41 views

Using proportional data with a binomial error structure in R… a worked example needing answers!

I am trying to test if the proportion of herbivores in spider's diets is related to the proportion of herbivores in their grassland, but am struggling to understand if I should be using a binomial ...
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1answer
70 views

Solving formula for confidence intervals on two proportions

I'm interested in comparing two independent proportions from two samples. The formula for doing so is available in the Internet (e.g. here). So far, so good. But my main purpose is not to build a ...
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Does $\sqrt{n}(Y_n-1)$ converge in distribution?

Let $n\in \mathbb{N}$ and consider, for each $n$, independent real valued stochastic variables $Z_{1n}\ldots Z_{nn}$, such that $$ P(Z_{nk}=n)=1-P(Z_{nk}=0)=\frac{1}{n} $$ for $k=1,\ldots,n$. Thus ...
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Show that $P(X \ge r ) = P (Y \le p)$ [duplicate]

Let $ X \sim \text{Bin}(n,p) $ and $ Y \sim \text{Beta}(r,n-r+1) $. Show , without integration by parts, that $P(X \ge r ) = P (Y \le p)$. From which point of view I answer this question.
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3answers
66 views

Negative Binomial Regression?

I have a dependent count variable that measures the number of days spent in a hospital (LOS) for a group of patients who received two different medical interventions upon hospitalization. I'm trying ...
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1answer
55 views

what is the Probability of selecting 10 SNPs from a list of 5000 SNPs simply by chance

We conducted a study to predict deleterious mutations from a list of around 5000 mutations (which contains both neutral and deleterious mutations; the real state of each mutation is unknown), using ...
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18 views

Standard error for aggregated proportions

In order to obtain confidence intervals for proportions I'm trying to calculate the standard error, but I'm having difficulty working out what N should be in a case such as mine. My data is such that ...
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1answer
26 views

Confidence Intervals for a relative risk where i lack the underlying data

I have two estimated rates and their 95% confidence intervals but not the underlying data. I take the ratio of the two to get a relative risk, but how do I determine the 95% confidence intervals for ...
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1answer
46 views

Has the free kick spray in soccer an effect? Binomial Testing

In Germany a referee supported the use of the free kick spray introduced on the World Cup 2014. He reported some statistics. His data supported the assumption using the spray leads to more goals after ...
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2answers
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What coefficients do I use for a binomial distribution problem?

I'm studying for an exam and my study guide explained combinations, permutations, and binomial distributions, but didn't cover much how to recognize where each comes into play in problems. I'm having ...
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35 views

Independent events in sequence

If I flip a fair coin twice, the probability of at least one Head is 0.75 (HH, HT, TH and TT). I flip the coin once and it lands Tails. In order to get at least one Head, the probability of the ...
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107 views

Show that if $X \sim Bin(n, p)$, then $E|X - np| \le \sqrt{npq}.$

Currently stuck on this, I know I should probably use the mean deviation of the binomial distribution but I can't figure it out.
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1answer
71 views

Residual variance for glmer

I am running a glmer model and I want to determine the total variance. My data is for survival and it is coded as 0 and 1, where 1 represents that the individual survived and 0 represents that the ...
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0answers
29 views

Mixed logistic model with complete separation

I want am trying to produce a mixed logistic model but certain explanatory variables suffer from complete separation. I am aware that I need to either use exact logistic regression or a firth ...
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2answers
55 views

Is it possible to model the conditional expectation of a binary outcome using an additively-separable link function?

Logit and probit link functions aren't additively separable. So, fitting a model using these link functions implies that the effect of one predictor in determining the outcome is not independent of ...
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1answer
31 views

multi stage binomial “process”

I wish to model the retransmission time of a file that divided into K blocks. I know the successful blocks of first transmission obey the binomial distribution $$ X_1 \sim \text B(K,p) $$ , p is the ...
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39 views

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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23 views

A binomial test with repeated measures?

I'm working on a study with a single trained animal (ie. our only participant). He is making a binary choice on a number of consecutive trials (we are essentially trying to teach him a rule -- if A, ...
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Test statistic and C.I. for population proportion

I'm doing a test statistic and C.I. for population proportion. Can someone explain to me what are assumptions coming from hypergeometrical distribution directly to normal distribution? As I ...
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1answer
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Test equality of binomial variances across four groups

I have four 100x1 vectors of binary outcomes of a particular experiment. I want to test for equality in variance across all of the four different treatment groups. At the moment I have used the ...
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2answers
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Determining unusual binomial results from a sub-population

If I have a population of 1948 students with a success rate of .154 (301 successes) and I break the 1948 students into their respective majors, how to I determine if the sub-population success rate is ...
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32 views

Reduce the polynomial terms in logistic regression (glm)

I've three categorical variables A, B and C with 5 levels each. The model I'm trying to fit is glm(Y~A+B+C, family=binomial()) How can I remove the higher order ...
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22 views

distribution of censored multinomial variable

Let $F$ be a multinomial random vector of $n$ trials in $k$ categories. Let the random vector $C$ be defined as \begin{equation}C_i \equiv \left\{\begin{aligned} 1 & \quad F_i>0 \\ 0 & ...
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1answer
37 views

Clarification on a paper regarding estimating N from a Binomial Distribution

I was wondering if someone could clarify the following for me. In the paper "Inference for the binomial $N$ parameter" by Adrian Raftery, his first example outlines the posterior of $N$ given $x$ as ...
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133 views

How to calculate confidence limits for various scenarios when drawing random cards from a pack?

I'm designing an experiment that involves a subject attempting to determine various attributes of a playing card drawn at random from a standard 52 card pack. The experiment is in four phases: ...
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22 views

Finding n and c in single sampling plan

I am learning a quality control course and in Single sampling scheme for attribute type inspection I don't understand the method used for calculating the values of $n$ and $c$. The method is as ...
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322 views

Logistic Regression - Error Term and its Distribution

On whether an error term exists in logistic regression (and its assumed distribution), I have read in various places that: no error term exists the error term has a binomial distribution (in ...
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22 views

What method to use in this cancer problem?

I am confused on what to do with this problem: "Suppose we identify fifty 50-to 54-year old women who have both a mother and sister with a history of breast cancer. Five of these women themselves ...
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22 views

Comparing the difference in proportions for 3 different groups

I conducted an experiment and just need some general guidance on where to go from here. I know I have to do some kind of binomial test on my data. Suppose I have the following data: ...
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1answer
318 views

Exact two sample proportions binomial test in R (and some strange p-values)

I am trying to solve the following question: Player A won 17 out of 25 games while player B won 8 out of 20 - is there a significant difference between both ratios? The thing to do in R that ...
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1answer
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Computing mixture of Binomial distributions

I'm trying to model a simple Bayes net, with $n$ samples based on a (unobservable) Bernoulli parameter, representing a true state of the world. Let $T$ be a Bernoulli random variable, with ...
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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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193 views

Estimating parameters for a binomial

First of all I'd like to precise that I'm not an expert of the subject. Suppose to have two random variables $X$ and $Y$ that are binomial, respectively $X\sim B(n_1,p)$ and $Y\sim B(n_2,p),$ note ...