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Questions tagged [normal-distribution]

The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is one of the most important distributions in statistics. Use the [normality] tag for asking about testing for normality.

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20 views

check for noncorrelation of normal pseudo random numbers using scatterplot

pseudo random number generators should give as output random sequences u1, u2, ... that are independent and identically distribuited (iid). Since testing for independence is not easy, the first check ...
42 views

Normal Distribution mean

What does it mean when we say "consider a normal distribution in variable $x$ whose mean is a linear function $Ay+b$ of second variable $y$"? As per my understanding there is 1 mean of a normal ...
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Question about the log-normal distribution

Let's say that $Y = X + Z$, with $X$ and $Z$ being independent, and $Y$ having the same distribution as $Z^2$. In addition, $X \geq 0$ and $Y, Z \geq 1$. The latter condition is needed for reasons ...
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Which data is “more normal”?

I have two sets of data, and I want to test which is "more normal" (specifically residuals from two different models fitted to hourly and daily data - the daily data is the hourly data aggregated). ...
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if the mode of a normal distribution is 0, then what's the value of the mean

so if the PDF attains its maximum at 0 it means that $f'(0) = 0$: $$f'(x) = -\frac{x}{\sigma^2 \sqrt{\pi}}\exp({-\frac{(x - \mu)^2}{2\sigma^2}})$$ $$f'(0) = 0 \iff 0 =0$$ yep, no valuable ...
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How to get Variance from Gaussian distribution and Random Initialization

I am following deeplearning.ai's videos on Coursera. Prof Ng mentions that specific random initialisations for the weights(for example, by Xavier or He initialisations) can help optimise learning. ...
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Time Series assumptions for iid $\epsilon$

thanks for reading my post. I know its fundamental and rather easy qns but I'm seriously struggling. Please help me, thank you very much! Let $\boldsymbol{X}$ have a distribution with mean $\mu$ and ...
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Time Series Analysis: Determine Which Value Will Be Hit First?

I am analyzing a time series of sales data, and calculating probabilities of certain targets being reached with the assumption that the distribution is normal (Essentially use a ...
257 views

Hypothesis testing- with normal approximation

In Europe the diameters of women's rings have mean 18.5 mm .Researchers claim that women in Jakarta have smaller fingers than women in Europe .The researchers took a random sample of 20 women in ...
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What is the intuition behind pi in the PDF of a Normal Distribution ? Is it related to some sort to a circle / sphere

The PDF of a Normal distribution is given as below I am aware of the various properties of Normal distribution and how the two parameters mu and sigma affect the shape of the distribution. What is ...
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Distribution of sum of cubes [duplicate]

If a set of $k$ random variables $x$ is drawn from the same normal distribution with mean $μ$ and standard deviation $σ$, then: the mean of the distribution of $Σx$ is $kμ$ the mean of the ...
39 views

MLE for bivariate normal data with known error variances

I am working with a set of bivariate data arranged into columns labelled 'x' and 'y'. I also have measurements for the error variances corresponding to each observation, labelled 'sx' and 'sy'. An ...
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Which test is suitable in below situation?

I want to calculate the correlation of two continuous variables, unfortunately both of them are not normally distributed. (by using Shapiro-Wilk test) There are two categorical confounding variables ...
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Mean of repeated samples

Let's assume we have random variables $X_1\sim N(\mu_1,1),\cdots,X_n\sim N(\mu_n,1)$. Now we take one sample from each and get $X_1 = x_1,\cdots,X_n = x_n$. We order them and calculate the mean of top ...
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Sensitivity analysis of an equation in R language [closed]

I have the equation, Y = A*B*C/(D*E) Where A, B, C, D and E are the certain parameters of 1000 samples (say groundwater samples). ...
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linear combination and univariate normal

Show that $(X_1,X_2)$ has a bivariate normal distribution with means $\mu_1, \mu_2$, variances $\sigma _1^2$ and $\sigma _2^2$, and correlation coefficient $\rho$ if and only if every linear ...
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Conjuage priors for linear combination

My knwoledge of statistics in general and Bayesian statistics in particular is limited. With that in mind, I would sincerely appreciate if somebody could help me with the following problem that I have ...
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What distribution can be predicted more accurately?

I am working on simple statistical prediction. However, whatever i did, i come up with a high range. I have used standard deviation and also percentile. Yes they work well in the given data but the ...
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How to find probability of quantiles given mean and variance? [closed]

If someone could explain the process for beginning this and the formulas involved I would be grateful. Male height in the Netherlands is normally distributed with a mean of 73 inches and a ...
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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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Will changing the standard deviation affect the distribution?

Let's say I want to generate some random data that follows the normal distribution, with a mean of 5. Will setting the standard deviation to 3 or 5 affect the distribution, that is, will it still ...
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What is the standard deviation and mean of the reciprocal of normal distribution in terms of that of the normal distribution? [duplicate]

What is the standard deviation and mean of the reciprocal of normal distribution in terms of the standard deviation and mean of the normal distribution?
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Is it possible to get equivalences of Western Electric Rules in non normal distribution with percentile values?

I am not a statistician and I am a bit lost with these concepts, but I will try to explain my situation. I have a non-normally distributed data, and I am trying to apply the Western Electric Rules to ...
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Why does the marginal likelihood integral have no closed-form solution?

In Bayesian inference we end up with the formula: $$P(\mathbf{w|t,X)}= \frac{P(\mathbf{t|w,X)}P(\mathbf{w)}}{\int P(\mathbf{t|w,X}) P(\mathbf{w}) d\mathbf{w}}$$ Assume the prior $P(w)$ is a ...