Tagged Questions

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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6 views

Wavelet transform of Gaussian function [on hold]

What is the wavelet transform of Gaussian function? Any continuous wavelet can be used.
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1answer
70 views

Area within a given number of standard deviations from given mean

I have a variable with mean value of 18.85 and standard deviation of 1.45. I want to define the area that is covered by 1.45 standard deviations left and 1.45 standard deviations on the right side ...
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2answers
31 views

Why do we estimate population parameters using statistic?

I had been studying statistics, I have a doubt that I couldn't find the answer of. Its related to estimating population parameters using statistic. Suppose we have a population size of 10000, we want ...
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0answers
19 views

Sampling from a portion of the normal distribution?

I have a a conditional distribution $p(X_1 | \theta) \propto MVN(\mu, \Omega) \pi(X_1)$ where $X_1=[x_1, x_2, \dots, x_n]'$ and $\pi(X_1)=1$ when all $x_i \in [0,a)$ and $0$ otherwise. Is there any ...
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0answers
22 views

How to check $H_0$ hypothesis using Pearson's criteria?

How to check hypothesis by using Pearson's criteria, that $H_0:$ random variable $X$ is normally distributed given that $k=7$ (count of intervals) and $\alpha=0.1 $ (significance level). I do ...
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0answers
15 views

Bimodality after Box-Cox Transform [on hold]

I have a data set that I need to transform to make it look more normal. This data will not be modeled using linear regression since it is not possible to measure response data. Instead, we are using ...
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0answers
7 views

Marginalizing product of multivariate normal distributions

How should I marginalize $F_{i}$ from the following probability distribution $$p(y_{i}|F_{i},\alpha, \Lambda, \Phi, \Sigma) = N(\alpha + \Lambda F_{i}, \Sigma)$$ in order to obtain ...
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1answer
28 views

Sampling according to a difference of two normal distributions

Assuming that I have two normal distributions $p_1(x)$ and $p_2(x)$ and I can draw samples efficiently from them. Now, I can easily draw samples from $p(x) = 0.5 p_1(x) + 0.5 p_2(x)$ by with ...
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1answer
23 views

Hypergeometric approximated Normal/Gaussian distribtuion

A large lecture theater has 270 seats, 24 of which can accomodate left-handed students. Suppose it is known that 14% of people are left-handed. One class held in the theater has 205 students. (a) ...
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1answer
25 views

Multivariate normal with singular covariance

I'm an undergraduate student. I read about multivariate normal distribution in hogg and craig. And i wonder why the covariance is allowed to be positive SEMI-definite. I read this Normal distribution ...
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0answers
10 views

Normalisation formula applicable to one or more data items

I've created a recurrent neural network, to which normalised values are passed as inputs. The normalization formula is: $$\tilde{x_{i}} = \frac{1}{1+exp(-\frac{x_i-\bar{x}}{\sigma})},$$ where ...
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0answers
16 views

Calculate pdf of complex model

I'm trying to model the distribution of effects of mutations (let's call it s) in evolution but I'm stuck in generating the probability distribution function (pdf) for my model. So, my model is a ...
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1answer
56 views

What is the probability that a girl is taller than a boy, with boys ~N(68, 4.5) and girls ~N(62, 3.2)?

"Given that boys' heights are distributed normally $\mathcal{N}(68$ inches, $4.5$ inches$)$ and girls are distributed $\mathcal{N}(62$ inches, $3.2$ inches$)$, what is the probability that a girl ...
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1answer
66 views

Gaussian is conjugate of Gaussian?

Someone told me that, Gaussian distribution is conjugate to distribution because a Gaussian times a Gaussian would still be Gaussian distribution ? Why is that ? Say the following situation: $X\sim ...
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0answers
22 views

Fitting multiple normal distributions to sample data

I have a data set of (time, action)-tuples. Actions are typically performed at approximately the same times every day, and depending on what the action is it may be done multiple times per day. If I ...
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1answer
23 views

z-score and Normal Distribution

I have what is probably a pretty stupid question but for whatever reason I have not been able to find an answer so here goes.... It's my understanding that a z-score can only be calculated and ...
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1answer
27 views

Choosing Variance for Gaussian Prior

I'm relatively new to bayesian inference, and was trying to apply a bayesian model in a real-world scenario. Let me describe the model in brief: We have $N$ i.i.d. random variables $D =(X_1, X_2, ...
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0answers
8 views

Find Points that Break a mutli-valued Relationship

I am looking for a suggestion on how to answer a question, or what to read more about. I am sorry if I do not sound professional, I am not. First a contrived example. I have a table of 50 states in ...
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0answers
47 views

How to transform continuous data with extreme bimodal distribution

Is there a way to transform a continuous predictor variable (grant) that has a bimodal distribution into a normal distribution (see density plot below)? I have tried log(x+c), z-score and inverse ...
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0answers
14 views

Is it reasonable to utilize z-scores

I have empirical observations to be compared with discrete distributions of random values (generated according to random models). The shape of my random distributions is not normal(according to ...
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1answer
46 views

Fitting a Gaussian to a histogram when the bin size is significant

I'd like to fit a Gaussian to some experimental data that is binned (the binning is a result of the physical limits of the device). Importantly, the bin size is significant enough that the gaussian ...
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0answers
22 views

How to find normal quantiles?

A social psychologist interested in eating behavior wanted to divide students into four groups based on their eating proclivities. The four groups were those who were restrained eaters, moderately ...
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2answers
29 views

When to use a multivariate normal distribution?

I was reading Bayes Point Machine example from infer.net: http://research.microsoft.com/en-us/um/cambridge/projects/infernet/docs/Bayes%20Point%20Machine%20tutorial.aspx The problem is when we have ...
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3answers
14 views

Error Propagation

I come from a physics background where the only error propagation I've dealt with was in the lab using the simple formulas found here: ...
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1answer
53 views

Heckman 2-step Error Assumption

first question on StackExchange; thank you for having me. I am trying to really nail the intuition for the Heckman sample selection model. One little thing that is bothering me is the assumption ...
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2answers
80 views

Confirmation of normality using residuals from an linear regression

95% of my residuals from an linear regression lie within 2 standard deviations of the predicted values. Is this enough to confirm normality or could any other distributions have 95% of residuals that ...
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1answer
29 views

Noise removal from a dataset with a know distribution

If I have a dataset where it's points are drawn from a known distribution(For example a normal distribution) due to some noise the histogram doesn't reflect such a behavior (not necessarily skewed) ...
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0answers
26 views

p-values, prior probabilities

I've got a set of N normal independent normal distributions, each representing a signal. I also got a new data sample, a vector $v$ of size Nx1. Now let's say I compute the p-value using the ...
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0answers
17 views

Existence of a specific linear combination of independent random variables (stochastic representation of the flexible skew normal)

Suppose to have two standard normal variables $X$ and $Y$. I would like to find something as $Y= aR+\sum_{i=1}^k b_kC_k$ (1) (k can be 1,2 or whatever) where $a,b_1, \dots , k$ are appropriate ...
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1answer
41 views

Why make the distribution of a variable more symmetric?

One of the goals of re-expressing data values is to "make the distribution of a variable (as seen its histogram, for example) more symmetric. My question is: why is more symmetric data better for ...
2
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1answer
45 views

Weird pdf of a quadratic function of a N(0,1) variable: miscoding or big rounding error?

I would like to calculate the pdf of a random variable y defined by : y=c+b*x+a*x^2 The pdf is a non-central chi-squared distribution. For a>0, it should be equal ...
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1answer
37 views

Correlated random draws with graph structured correlation

I have a problem where I have a graph structure, such that some nodes are connected to other nodes i.e. we have an adjacency matrix of size n*n with a 1 corresponding to a connection and 0 otherwise. ...
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2answers
60 views

What is the mean of this exponential random variable?

I have read a paper that says that the following is exponentially distributed $$ Y= \bigl| \sum_{i=1}^n \gamma_i^{-\frac{1}{2}} h_i \bigl|^2$$ where $\gamma_i$ are non-negative constants and ...
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2answers
220 views

Is data distributed as a Gaussian?

I know there are methods to check whatever the observed data DOES NOT follow a Normal distribution. I'm thinking about chi-square test, Anderson test etc. Is there any function/test/metric which says ...
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0answers
45 views

Multivariate normal distribution

I am not able to figure out how to derive this.Kindly explain this step.
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1answer
25 views

Confused by notation for normal distribution

In my statistics course, we were taught that the normal distribution function can be expressed as $f(x; \mu, \sigma).$ However, I also sometimes see it as $X \sim N(\mu, \sigma^2)$ Are these the same? ...
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2answers
63 views

Re-estimating a probability distribution with additional priors

I have a 3D dataset with at least millions of data points (scatter events from atoms, approximately Gaussian). I am modeling this data with a Gaussian Mixture Model. The usual approach would be to ...
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0answers
28 views

Why there is no uniform prior for Box-Cox Power Transformed Normal Models

I am trying to get intuition why uniform prior like below will not work for the box-cox model. Box-cox model: $y^{(\phi)}_i \sim N(\mu, \sigma^{2})$ where $y^{(\phi)}_i = (y^{\phi}_i-1)/\phi $ if ...
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0answers
33 views

Cumulative Distribution Function For Normals

Suppose $X_1$ and $X_2$ are $N(0,1)$ random variables such that $X_2=-X_1$ if $|X_1|<1$ and $X_2=X_1$ otherwise. Obtain the cumulative distribution function of $X_1+X_2$ represented in the form(s) ...
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1answer
16 views

Variance of precision in conjugate prior

How can I calculate the variance of the precision in a normal distribution, knowing I used a conjugate prior?
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1answer
29 views

Probabilistic comparison of two mixture models?

Given two gaussian mixture models (GMMs) with different degrees of freedom, is there a way to determine the probability that one is generated from the other? That is, can we give a probability to the ...
0
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0answers
24 views

Generating two normally joint distributed Random Variables

If I generated two random variables with mean $\mu_1$ and $\mu_2$, but use the covariance matrix as the second parameter of the normal distribution - does this imply that the two variables are jointly ...
0
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1answer
35 views

I did this problem but I got percents as the answer not two values. What did I do wrong?

Suppose that the lifetime of a particular electronic circuit has a normal distribution with mean of 50,000 hours and a standard deviation of 8,000 hours. You select a random sample of 25 circuits 1) ...
4
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1answer
103 views

Sum of truncated normal with two normal distributions

Suppose I have one normal distribution $W \sim N(\mu_{w},\sigma_{w}^2)$ with a known cuttoff point (percentile) on this distribution called $c$. The first part of $W \in [-\infty,c[$ needs to be ...
7
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0answers
90 views

What Ratio of Independent Distributions gives a Normal Distribution?

The ratio of two independent normal distributions give a Cauchy distribution. The t-distribution is a normal distribution divided by an independent chi-squared distribution. The ratio of two ...
2
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1answer
47 views

Folded Normal and truncated Normal

Suppose to have a vector of random variables $\mathbf{y}$, distributed as a multivariate normal with mean vector $\boldsymbol{\mu}$ and covariance matrix $\boldsymbol{\Sigma}$. The variable ...
4
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1answer
87 views

Why is the sampling distribution of variance a chi-squared distribution?

The statement The sampling distribution of the sample variance is a chi-squared distribution with degree of freedom equals to $n-1$, where $n$ is the sample size (given that the random variable of ...
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0answers
10 views

How do I determine sample size to validate a requirement when I have a lot of margin?

I apologize if a similar question has been asked, but my search has yielded no results. I am having some trouble nailing down the correct methodology to use to design an experiment I am working on. ...
2
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2answers
68 views

What characteristics should a distribution have for CLT to work?

If a "distribution" is constant, then CLT is not going to work, obviously. However, even if it is not a constant, but variance is very small, the distribution of the sums is still not normal. For ...
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0answers
31 views

Two Gaussian Likelihoods with Two Decision Boundaries , 0/1 loss function

we assume that Y := {1, 2}. Then our decision can be re-written as y ∗ = {1 if p(x|y = 1) > p(x|y = 2) , 2 otherwise} with a decision boundary at p(x|y = 1) = p(x|y = 2). How can we construct an ...