Questions tagged [normal-approximation]

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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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4 votes
1 answer
135 views

Convergence in distribution for difference in sample means?

Suppose $X_i, i=1,\ldots, n$ are $i.i.d.$ random variables with mean $\mu_X$ and variance $\sigma^2_X$ $Y_j, j=1,\ldots, m$ are $i.i.d.$ random variables with mean $\mu_Y$ and variance $\sigma^2_Y$ $\...
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Constructing a Confidence Interval using the normal approximation of a poisson

Letting Y₁ ... Yₙ ~ Pois (λ), this would approximate to N(λ,λ). Hence constructing a confidence interval with a 90% confidence level would be: $$0.90 = (Z₀.₀₅ < \frac{Ȳ -λ}{\sqrtλ/n} < Z₀.₉₅) = (...
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133 views

Binomial AB Test - binomial test vs normal approximation

I want to run an ab test on two groups of people If I use the binomial test I get a p-value of 0.007355 ...
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1 vote
1 answer
41 views

Normal approximation and Hoeffding bound

Hoeffding bound for any $\epsilon>0$ is: $$P_F(|\bar{X}_n-\mu(F)|\geq \epsilon)\leq 2 \exp\{-\frac{n\epsilon^2}{2}\}=h(\sqrt{n}\epsilon)$$ wherever $|X|<1$. Now I want to have a comparison ...
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2 votes
1 answer
228 views

Can Student's t-distribution be used in Normal Approximation to Binomial?

The question nearly covers it all. I clearly have a binomial distribution, however the variance and standarddeviations are unknown, the population is also just ...
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1 answer
68 views

Central Limit Theorem Approximation and Relation to Law of Large Numbers

Assume the Linberg-Levy CLT to where we know $$\sqrt{n}\frac{\bar{X}_n-\mu}{\sigma}\xrightarrow{d}N(0,1).$$ I feel like I commonly see then that $$\bar{X}_n\approx N(\mu,\frac{\sigma^2}{n}),$$ but ...
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1 vote
1 answer
124 views

Mann-Whitney Normal Approximation process help

Let $X_{1}, X_{2}, ..., X_{n}$ is i.i.d sample from $X$ and $Y_{1}, Y_{2}, ..., Y_{m}$ is i.i.d sample from $Y$. And both samples are independent each other. Trying Mann-Whitney U-test then, $U =$ $\...
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3 votes
1 answer
739 views

What is the difference between normal approximation and poisson approximation of binomial distribution?

what is the difference between Poisson distribution as an approximation of Binomial distribution and Normal (Gaussian) distribution as an approximation of Binomial distribution? Both are ...
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1 answer
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How normal is the following distribution of data? [closed]

I'm using the following dataset with 2 columns (features) and 1 label to train a Gaussian Naive Bayes classifier. How would you determine (using a stastiscal normality test) whether the data is ...
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1 vote
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Approximating a distribution with normal

Let's say I generated samples from a distribution $f$ whose functional form I do not know. I want to approximate this distirbution with a multi-variate normal. We know that if samples are generated ...
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1 vote
1 answer
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How does Normal approximation work when ties exist for Wilcoxon Signed rank test?

I ran wilcox.test() in R (outcome variable was a test score and the data was paired samples) and got a warning message saying that it cannot generate a p-value for tied values. I saw the R document ...
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0 answers
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at what probability will the probability we start considering the data?

For example I have this problem, Do Americans tend to vote for the taller of the two candidates in a presidential election? In 30 presidential elections since 1856, 18 of the winners were taller than ...
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5 votes
2 answers
143 views

What is the correct terminology for repeating groups of coin flips multiple times in a simulation?

I previously posted a question that is causing a lot of confusion because my terminology is incorrect. I decided to post this question to ensure I am starting my problem with the correct terminology. ...
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20 votes
4 answers
4k views

Why does increasing the sample size of coin flips not improve the normal curve approximation?

I'm reading the Statistics (Freeman, Pisani, Purves) book and I'm trying to reproduce an example where a coin is tossed say 50 times, the number of heads counted and this is repeated say 1,000 times. ...
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2 answers
87 views

Normal Approximation to Binomial Question

I am having issues solving the following problem: A recent study found that cedar trees by indigenous settlements grow taller than cedar trees not by indigenous settlements. The probability of a ...
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1 answer
169 views

Normal approximation on (what it looks like) a poisson

I am self-studying inferential statistics from Larson's introductory textbook named: "Introduction to Probability Theory and Statistical Inference" (1st edition John Wiley & Sons.). I came ...
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4 votes
1 answer
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How to calculate confidence interval of incidence rate under the Poisson distribution

I'd like to be able to calculate the confidence interval for an incidence rate under the Poisson distribution. I am inclined to use a normal approximation formula (the Wald interval) which is $\text{...
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2 votes
1 answer
1k views

Lower Bound on the Total Variation Distance between two Binomials

Let $X= B(n,1/2)$, $Y=B(n,1/2 + \delta)$, for a small $\delta >0$ be two Binomial Distributions. Question 1. I am looking for a lower bound on the Total Variation Distance the two Binomials ...
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2 answers
151 views

A box contains 48 tickets [1] and 52 [0]. If you draw 10 times at random and with replacement, what is the probability of getting a sum of 3 or less?

I came across a question like this and I try it to solve it by 2 different methods. However, these 2 methods don't yield the same answer. So, I'd like to ask you what am I missing. I'm clearly doing ...
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0 answers
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How to test proportion against 1 - null hypothesis: H0: p=1

My research question: I have a data set with good observations and bad observations and have to estimate if all observations are good in the population with 99% confidence. My suggested method: My ...
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-1 votes
1 answer
93 views

Approximate meaning of probability? [closed]

After the football match each football fan leave on the stadium 2 empty bottles. The janitor finds the bottle with probability 0.3. Find the approximate meaning of probability that the janitor ...
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7 votes
0 answers
143 views

Bayesian inference via approximate data likelihood

Suppose that we have a very large i.i.d. sample $x_1,...,x_n$ and a data likelihood defined by $$p(x | \theta,\beta) = \prod_ip(x_i | \theta,\beta)$$. Further suppose that $\theta$ is the parameter ...
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1 vote
1 answer
350 views

Asymptotic (normal approximation) distribution of the division of two means of exponential random variables

Suppose $X_{11}, ...X_{1n}$ are iid rvs following an exponential distribution with expectation $\mu_1$, and $X_{21}, ...X_{2n}$ are iid rvs following an exponential distribution with expectation $\...
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0 votes
1 answer
82 views

Combined confidence of hit/miss results from 20 different test subjects

I'm a computer science student and statistics isn't my strong suite. I would appreciate some help. I did a task performance experiment for my Master's thesis to validate my "special secret algorithm"....
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  • 101
3 votes
1 answer
383 views

Hypothesis test of 2 proportions, with $np < 5$

We are frequently conducting one-tailed hypothesis tests for 2 proportions ($H_0: p_1-p_2=0;\, H_1: p_1-p_2 > 0$). However, $p_2$ is relatively small in terms of $n, x$ and in some cases we find ...
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  • 141
7 votes
1 answer
300 views

Berry-Esseen Theorem with Continuity Correction

Given independent but non-identical random variables $X_1, X_2, \ldots ,X_n$ with $E[X_i]=0,$ $E[X_i^2]=\sigma_i^2=1$ and finite absolute third moments $\rho_i=E[|X_i|^3].$ Let $$S_n = {\sum_{i=1}^n ...
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