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 Qn [on hold]

Given X~N(20, 16), find a) the value of k such that P(x < k) = 0.2758 b) the value of k such that P(x > k) = 0.1539 How do I solve this?
6
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1answer
59 views

How to calculate probability of observing a value given a permutation distribution?

I have a single observation with value $x = 0.5$ that comes out from a complicated computational process. I would like to know what is the probability to observe such value by chance. To attempt to ...
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0answers
20 views

Constructing a normal probability plot template in Excel [on hold]

How can I create a blank normal probability plot template in Excel? I need to use a paper version in a very rough atmosphere. There is a blank example at this website which I like. ...
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0answers
33 views

4 cases of Maximum Likelihood Estimation of Gaussian distribution parameters

Let $x_1,x_2,...,x_n$ some normally distributed observations. So $\vec{x}=\begin{bmatrix}x_1 & x_2 & ... & x_n\end{bmatrix}^{T}$ In the context of my research I am trying to estimate ...
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0answers
22 views

What is the probability of at least one of a sum of normally distributed variables being greater than a threshold?

Let's say I have a pencil factory. I don't mind if my pencils are too short, but it's important they're not too long. My Quality Control department measure each pencil, and their measurement will be ...
3
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1answer
87 views

Transform normal distribution to skewed distribution without changing its support

I've found many questions and answers about transforming skewed distribution to normal. This question might arise because the simplicity of working with normal data. But, is there any function that ...
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0answers
51 views

How do I solve a under-determined quadratic multi-variate system?

I performed some simulations with known values of input variables $X_1$, $X_2$ and $X_3$, to find output response $Y$. The variables are distributed as following: $$ X_1 = N(\mu_1, \sigma_1) $$ $$ ...
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1answer
53 views

Does p value below 0.05 in mvShapiro.Test mean multivariate normality or not?

I am performing mvShapiro.Test from mvShapiroTest package. I get ...
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1answer
37 views

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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0answers
12 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
88 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
60 views

Assumptions behind simple linear regression model

Let's say we have a 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 1 ...
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0answers
15 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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0answers
36 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
19 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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2answers
110 views
+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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0answers
22 views

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
21 views

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
107 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 ...
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0answers
20 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
42 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
284 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
184 views

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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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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0answers
50 views

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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0answers
14 views

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, ...
2
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1answer
49 views

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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0answers
20 views

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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1answer
70 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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0answers
9 views

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 ...
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1answer
85 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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1answer
269 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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1answer
33 views

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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0answers
10 views

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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1answer
64 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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2answers
465 views

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 ...
2
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1answer
73 views

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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1answer
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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1answer
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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19 views

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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27 views

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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18 views

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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43 views

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 ...