The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is often used as a reference against which other distributions are compared.

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Normal distribution in R: Find the value of $x$ for $P(X=x) = c$ where $c$ is known

I have a normal distribution with parameters $\mu=750$, $\sigma=260$. I'm interested in finding the value of $x$ that satisfies $P(X=x)=0.001$ for both sides of the tail. How would I go about doing ...
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10 views

Evaluate normal distribution at point one standard deviation away

Assume I have given a one-dimensional normal distribution with some $\mu$ and $\sigma^2$. Now for a given $x$ I want to decide if it is not more than one $\sigma$ away from $\mu$. I thought it is ...
7
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1answer
82 views

Generating samples from singular Gaussian distribution

Let random vector $x = (x_1,...,x_n)$ follow multivariate normal distribution with mean $m$ and covariance matrix $S$. If $S$ is symmetric and positive definite (which is the usual case) then one can ...
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1answer
44 views

Assumtions behind simple linear regression model

If we are taking about simple linear regression model, that is, $y = X\beta + r$ where $y$ is a vector of size n x 1, $X$ a matrix of size n x p, $\beta$ the regression coefficient vector of size p x ...
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14 views

Gaussian Distribution for Latitude/Longitude Coordinates

I have a bunch of latitude/longitude coordinates and if I plot it on a map, it seems to follow a bivariate distribution. I would like to estimate the distribution of points using a bivariate ...
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35 views

Normality distribution

I try the shapiro.test for my transformed dataset (logarithm). I obtain p value 0,0001207. I try to draw the graph of ditribution and obtain this graph (I attached). For you, do I have a normal ...
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1answer
18 views

chi-squared to test if two variables have the same frequency distribution

I want to test if x and y have the same frequency distributions using chi-squared. In my code below, I've concluded that because ...
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+100

Information about normal distribution

Is it fair to assume that this values have a normal distribution? Frequency of clock of a CPU [I have 100 observations between 100 Mhz and 4Ghz] Ram of a Computer [I have 150 observations between ...
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Biostatistical question [closed]

Hemoglobin level of pregnant women follows a normal distribution distribution. If 40 out of 1000 women and 200 out of 1000 have hemoglobin less than 9 and 10 respectively, find the mean and standard ...
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0answers
14 views

Standard deviation from difference between percentile [closed]

Assuming that the underlying distribution follows the normal distribution, if we are given a difference of aX (units of another random variable) between the 2d percentile and the 98th percentile of Y, ...
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0answers
18 views

Find the area under the standard normal curve? [closed]

Find the area under the standard normal curve which lies a.) to the left of $0.47$ b.) to the right of $z=-0.06$ c.) to the right of $z=2.53$ d.) to the left of $z=-1.31$ e.) between $z= 0.72$ and ...
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3 correlated questions: Find the roots of an equation, find the inverse of a function and find the c.d.f. of a function of a random variable

I have 3 correlated questions: Find the roots of an equation, find the inverse of a function and find the c.d.f. of a function of a random variable. The questions are in the picture. Sorry for the bad ...
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1answer
49 views

When is 'grading on a curve' appropriate?

Wikipedia defines 'grading on a curve' as a a statistical method of assigning grades designed to yield a pre-determined distribution of grades among the students in a class. The article does ...
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2answers
172 views

Probability of agreeing to do some work depending on the payment

I am looking for several options of modeling the probability of people agreeing to do some work depending on the price/payment. The payment can only range between p1 and p2 (p1 < p2). I looked at ...
5
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1answer
67 views

Are group effects in a mixed effects model assumed to have been picked from a normal distribution?

Say we're interested in how student exam grades are affected by the number of hours that those students study. We sample students from several different schools. We run the following mixed effects ...
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3answers
105 views

How large does a Poisson distribution's mean need to be to use normal distribution statistics?

As the mean of a Poisson distribution increases, the Poisson distribution approximates a normal distribution. I assume that once the Poisson mean becomes large enough, we can use normal distribution ...
2
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0answers
18 views

Box Muller vs Numpy?

I used the Box Muller transform and pythons uniform random number generator to sample random numbers in a given interval [a,b]. Here's the approach I used: Note: I know the average and the standard ...
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1answer
40 views

Transforming a Random Variable's distribution to Normal using Z-Scores

I have a random variable and many observations of that variable. The random variable is not normally distributed; its distribution is unknown. However, to analyze this variable and construct a time ...
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2answers
283 views

Calculating SD for normal distribution with only mean and 5% and 95% quantile values

As part of a Bayesian method to estimate the divergence times of species, priors have to be set with values based on previous literature or known fossil dates. These priors can have different ...
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4answers
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Is this correct ? (generating a Truncated-norm-multivariate-Gaussian)

If $X\in\mathbb{R}^n,~X\sim \mathcal{N}(\underline{0},\sigma^2\mathbf{I})$ i.e., $$ f_X(x) = \frac{1}{{(2\pi\sigma^2)}^{n/2}} \exp\left(-\frac{||x||^2}{2\sigma^2}\right) $$ I want an analogous ...
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0answers
21 views

Bootstrap procedure with estimates from EM

I'm a little lost on this, but my question is I implemented an EM algorithm to estimate means and variances of normal distribution, but now I need to implement a bootstrap procedure to estimate the ...
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1answer
42 views

How to measure the difference of a distribution being normally distributed

Imagine I have a distribution like the following File SkewedDistribution.png of Wikimedia Commons by User:Audriusa licensed under CC-BY-SA 3.0 Now I want to measure, how this distribution differs ...
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Why is my (own) shapiro test inaccurate?

Linked to my previous question : From moments product matrix to covariance matrix of normal order statistics , i coded an EXACT shapiro-wilk test for normality. Using the related literature; i coded ...
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How to find the probability distribution that one variable equals another in a Gaussian Mixture Model

I have a multi-dimensional Gaussian, and I want to find the distribution for the case that some variables are a linear function of the others. For example, in the case of a two-dimensional Gaussian, ...
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1answer
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From moments product matrix to covariance matrix of normal order statistics

I'm trying to compute the exact covariance matrix of normal order statistics. Well known formulas (listed in Zakkula Govindarajulu, 1962) allow us to compute moments of order statistics, as well as ...
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How to use a normal log-likelihood function to estimate the variance?

I have an array of data that is normally distributed, i.e. we're dealing with a multivariate Gaussian. We write the data as $X = \{x_1, x_2, \ldots , x_N\}$ So, there are unknown parameters $\mu$ and ...
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43 views

Fourier transform and the multivariate normal

I am wondering about how to specify multivariate normal distributions for vectors that have undergone a Fourier transform. For instance: Say we have the mean vector $\boldsymbol{\mu}$ and covariance ...
2
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1answer
67 views

rnorm vs dnorm in R

In human language the rnorm(n=1000, m=24.2, sd=2.2) returns the random numbers which follows normal distribution. Another explanation could be that it returns ...
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1answer
23 views

What is the dimension of the Gaussian log-likelihood function?

I am having trouble comprehending the log-likelihood of a multivariate normal distribution. For an n-dimensional vector $\mathbf{r}$ of N i.i.d. data points $\mathbf{r}=(r_1,...,r_N)$, the ...
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How to understand a Gaussian likelihood function vs. the variance of data points? [duplicate]

This is an elementary question, but I find myself very confused visualizing this (if there are errors in anything below, please correct me): The likelihood function describes the probability density ...
2
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1answer
83 views

MCEM algorithm in normal distribution

Consider $z_1,\ldots,z_n$ as a sample of observations of $Z$ and $y_1,\ldots,y_n$ the missing data, where $Z\sim N(\mu,\sigma^2+1)$ and $Y\sim N(0,1)$. i)Find the expression of ...
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267 views

What is exactly distributed according to t-distribution?

I try to understand the idea behind the t-distribution. Here are the steps that I have understood so far: We use a sample of N elements to estimate the population mean. In more details, we use the ...
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How accurate is my simple description of a confidence interval?

Here's my simple words-only description of a 95% confidence interval for the mean. How accurate is it? the sample mean comes from a distribution of possible sample means the sample mean might have ...
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How to compute the likelihood of a sample within a process containing gaussian and Non-gaussian noise

First, I'm sorry if the topic doesn't reflect the essence of my question very well, I don't have a very good statistical background. I've got a random variable, that is subject to two sources of ...
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63 views

Berry-Esseen bound for binomial distribution

From the Berry-Essen theorem I can deduce $$\sup_{x\in\mathbb R}\left|P\left(\frac{B(p,n)-np}{\sqrt{npq}} \le x\right) - \Phi(x)\right| \le \frac{C(p^2+q^2)}{\sqrt{npq}}$$ with $C \le 0.4748$. My ...
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Transforming Data: All variables or just the non-normal ones?

In Andy Field's Discovering Statistics Using SPSS he states that all variables have to be transformed. However in the publication: "Examining spatially varying relationships between land use and ...
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1answer
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Joint probability density function

I'm stuck with this question: Suppose I have two random variables: A and B such that $$A\sim N(\mu_A,\sigma_A)$$ $$B\sim N(\mu_B,\sigma_B)$$ A and B are independent. I create a new random variable ...
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75 views

Is this a normally distributed time series?

I have these data, representing a time series of the sales of a product: 1485, 1068, 1368, 1236, 1926, 1550, 2249, 800, 1712, 1734, 1348, 1875 The skewness of ...
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29 views

Conditional Expectation of a product and sum of three Gaussian Random Variables

I have a problem and I have no idea how to tackle it. Any help would be greatly appreciated. The problem is the following: Assume I have three mutually independent random variables $a$, $b$, and $c$, ...
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1answer
45 views

Prove that the distribution of $Q$ is chi-squared with $p_2$ degrees of freedom

Suppose $X$ is a $p$-dimensional vector following $N_p(\mu,\Sigma)$ distribution, where $\mu$ is $p$-dimensional and $\Sigma$ is $p\times p$. Let $X=\left(\begin{array}{ccc}X_1\\X_2\end{array} ...
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Statistical Significance Without Normal Distribution nor Equality of standard deviation

I have two datasets consisted of 4 columns. I have to measure if the differences among the data (each column represent another data) are statistically significant. The problem is that: in the first ...
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So survey data cannot be normal distributed?

I am analyzing a data from survey. The data is from a 2X2 between subjects experiment design with 45 subjects in each of the four conditionsThe questions are based on a 5-point or 10-point scale. ...
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1answer
34 views

Meaning of syntax $N(\mathbf{y} \mid \mathbf{0}, \mathbf{K})$ (multivariate normal distribution)

So I'm reading notes on Gaussian Processses, and came across syntax $p(\mathbf{y} \mid \text{stuff}) = N(\mathbf{y} \mid \mathbf{0}, \mathbf{K})$ for multivariate normal distribution, and I'm not ...
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Quality control - non-normal distribution

Suppose we have a production line, which makes widgets. Assume also that we know distribution of widget's length ~ $N(\mu, \sigma)$ We measure widget's length and if it is within $\mu+/- 2 \sigma$ we ...
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approximating order statistics of non-identical normally distributed random variables

Algorithm AS 177: Expected Normal Order Statistics (Exact and Approximate) provides an approximation of order statistics of independent identically normally distributed random variables. I want to ...
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Expected Euclidean distance between normal prior and posterior as sample size changes

Suppose the prior for some random variable $x$ is normal with mean $\mu$ and variance $v$. Denote the prior density by $f(x|\mu,v)$. Given normal likelihood with known variance $v$, the posterior for ...
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Jeffreys Prior for normal distribution with unknown mean and variance

I am reading up on prior distributions and I calculated Jeffreys prior for a sample of normally distributed random variables with unknown mean and unknown variance. According to my calculations, the ...
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1answer
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Conditional density of bivariate normal and normal

Let $Z=X+Y$ where $X \sim N(\mu,\sigma^2)$ and $Y \sim N(0,1)$ are independents. What is the conditional density of X given Z, $f_{X|Z}(x|z)$? I already found that ...
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Can we use normal distribution statistics on frequency distribution outputted by bootstrapping?

If I understand correctly, this is the bootstrapping procedure: Pretend sample is population Repeatedly resample from this pretend-population Calculate the mean of each resample. The output of ...