Questions tagged [normal-approximation]
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27 questions
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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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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:
$$0.90 = (Z₀.₀₅ < \frac{Ȳ -λ}{\sqrtλ/n} < Z₀.₉₅) = (...
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Binomial AB Test - binomial test vs normal approximation
I want to run an ab test on two groups of people
If I use the binomial test I get a p-value of 0.007355
...
1
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1
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114
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Normal approximation and Hoeffding bound
Hoeffding bound for any $\epsilon>0$ is:
$$P_F(|\bar{X}_n-\mu(F)|\geq \epsilon)\leq 2 \exp\{-\frac{n\epsilon^2}{2}\}=h(\sqrt{n}\epsilon)$$ wherever $|X|<1$.
Now I want to have a comparison ...
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Can Student's t-distribution be used in Normal Approximation to Binomial?
The question nearly covers it all. I clearly have a binomial distribution, however the variance and standarddeviations are unknown, the population is also just ...
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1
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141
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Central Limit Theorem Approximation and Relation to Law of Large Numbers
Assume the Linberg-Levy CLT to where we know
$$\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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2
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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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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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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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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
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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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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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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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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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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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260
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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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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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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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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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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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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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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)$$. Further suppose that $\theta$ is the parameter ...
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408
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Asymptotic (normal approximation) distribution of the division of two means of exponential random variables
Suppose $X_{11}, ...X_{1n}$ are iid rvs following an exponential distribution with expectation $\mu_1$, and $X_{21}, ...X_{2n}$ are iid rvs following an exponential distribution with expectation $\...
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Combined confidence of hit/miss results from 20 different test subjects
I'm a computer science student and statistics isn't my strong suite. I would appreciate some help.
I did a task performance experiment for my Master's thesis to validate my "special secret algorithm"....
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1
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615
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Hypothesis test of 2 proportions, with $np < 5$
We are frequently conducting one-tailed hypothesis tests for 2 proportions ($H_0: p_1-p_2=0;\, H_1: p_1-p_2 > 0$).
However, $p_2$ is relatively small in terms of $n, x$ and in some cases we find ...
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Berry-Esseen Theorem with Continuity Correction
Given independent but non-identical random variables $X_1, X_2, \ldots ,X_n$ with $E[X_i]=0,$ $E[X_i^2]=\sigma_i^2=1$ and finite absolute third moments $\rho_i=E[|X_i|^3].$
Let $$S_n = {\sum_{i=1}^n ...
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