Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [truncated-normal]

The truncated normal distribution is a normal (Gaussian) distribution that as been "cut off" at one or both ends.

0
votes
1answer
34 views

Dealing with measurements falling outside of the theoretical range/boundaries of the data

Imagine I am measuring a bounded variable (with a maximum possible value above which the data doesn't make sense) and I end up with the following dataset with my measurements and measurement errors as ...
4
votes
1answer
99 views

Compute truncated normal distribution with specific mean and variance

I have a simple setting: I simulate demand patterns that are distributed according to a truncated normal distribution with a given mean and variance after truncation. The truncation is from the left ...
1
vote
1answer
41 views

Linear Mixed Effects Models for Truncated Normal Distribution

I would like to analyze amplitude differences of discrete oscillations that were detected in a time-series using a thresholding method between three different conditions. The number of discrete events ...
7
votes
1answer
375 views

Calculating the expected value of truncated normal

Using the mills ratio result, let $X \sim N(\mu, \sigma^2)$, then $E(X| X<\alpha) = \mu - \sigma\frac{\phi(\frac{a- \mu}{\sigma})}{\Phi(\frac{a-\mu}{\sigma})}$ However, when calculating it in R. ...
0
votes
0answers
20 views

Variance of squared truncated normal

What is $$ \text{var}\left[v+\frac{1}{2} X \left(\frac{v-\mu}{\sigma}\right)^2 \mid v \leq \mu \right],$$ where $v$ is normally distributed $\mathcal{N}(\mu,\sigma)$ and $X>0$?
1
vote
1answer
44 views

Correlation between normal RV and truncated normal RV

If I have two normally distributed random variables $a\sim\mathcal{N}\left(\mu_a,\sigma_a\right)$ and $b\sim\mathcal{N}\left(\mu_b,\sigma_b\right)$ with correlation $\rho$, is there a closed form for ...
3
votes
0answers
99 views

IRLS for truncated normal GLM

I have data for which responses fall in $y \in [0,\infty)$ for which, it seems, the standard GLMs based on, say, gamma or inverse-Gaussian fail since they don't allow responses with values equal to 0. ...
1
vote
0answers
27 views

How can I test if a permutation hypothesis test produces valid results based on the probability distribution used?

I'm using the Join Count statistics to get insight if there is spatial autocorrelation in a categorical feature. I would like to test if the pseudo p-value returned comes from a valid hypothesis test ...
1
vote
0answers
38 views

How to sample a vector from Multivariate normal with the last element constraint to positive?

I'm doing MCMC simulation and a posterior is hard to sample. Suppose I need to sample a vector $\beta \sim N(M_{\beta} , \Sigma_{\beta})1_{\beta_{K}>0}$, which mean $\beta$ is a vector with length ...
0
votes
1answer
144 views

Is the truncated normal distribution symmetric?

I am running a Metropolis-Hastings MCMC to find the distribution of a parameter that takes real, positive values. I was considering using the truncated normal distribution, and was wondering if I have ...
0
votes
0answers
17 views

Conditional expectation of RVs under truncation-based stochastic signal release?

Suppose $z\sim N(0,1)$ and $x\sim N(\gamma z, 1)$, where $\gamma$ is a known sensitivity parameter. That is, $x=z+\epsilon, \epsilon \sim N(0,1)$ where $\epsilon$ is exogenous. Further, suppose there'...
5
votes
2answers
211 views

What is the distribution of min{0,X} when X follows some general normal distribution?

What is the distribution of $\min\{0, X\}$ when $X$ follows some general normal distribution?
5
votes
3answers
327 views

Expectation of truncated normal

Suppose I have a bivariate normal $(x,y)\sim \mathcal N(0,\Sigma)$ . Is there an easy formula for the expectation $\mathrm E(x\mid y>0)$ ?
1
vote
0answers
29 views

Can I consider this as a truncated normal distribution?

I have a variable whose maximum value is fixed (maximum number of days in the observation period). In some plots, the histogram of the log-transformed variable peaks near the maximum, but not at the ...
2
votes
0answers
119 views

Bayesian prior and posterior computation for a truncated normal

I have to deal with data in a Bayesian framework, ultimately devising a Gibbs sampler for inferring all my distributions parameters. Specifically, suppose I observe some univariate data distributed ...
0
votes
0answers
189 views

Estimate parameters from truncated normal sample [duplicate]

I have a question like this, $X \sim N(\mu,\sigma^2)$ with unknown parameters. Now, a sample of size $m$ generated from X, but filter by X < T, i.e., any number larger than T will be ignored and ...
2
votes
0answers
160 views

Truncated mulitvariate normal: first two moments

Let $X\in \mathbb{R}$ be a univariate random varible for which it holds that $$ X \sim N(\mu,\sigma^2).$$ where $\mu\in \mathbb{R}$ gives the expected value and $\sigma^2>0$ is the variance. If ...
3
votes
1answer
151 views

Numerical computation of the means and covariance in a truncated bivariate normal distribution

How can I compute the means and covariance of a truncated bivariate normal distribution? I am particularly worried about the case when the truncation occurs very far from the mean. Is there a robust ...
0
votes
0answers
123 views

Linear combination of truncated normals

I am trying to calculate the following expression: $$ Z = \mathbb{E}\left[\left| \langle \mathbf{a}, u \rangle \right| \right] = \left| \sum_{i=1}^d a_i u_i \right|, \quad \left\| u \right\| = 1 $$ ...
2
votes
2answers
99 views

How to find the mean of all z scores above a cutoff

I would like to find the mean of all z-scores above a z-score cutoff. For example, what is the mean of all z scores above a z of 1.96 in a distribution N(0,1). (My calculus skills are modest.)
2
votes
1answer
275 views

Moments of the truncated normal distribution (univariate) away from the mean

I need to compute the mean and variance of the truncated normal distribution. For simplicity, let us focus on a standard normal, since the general case can be reduced to this. The PDF is given by: $$...
4
votes
1answer
72 views

Sampling from multivariate normal conditional on a negative minimum

Let $X\sim \mathcal{N}(\mu,\Sigma)$, where $\mu\in\mathbb{R}^n$ and $\Sigma\in\mathbb{R}^{n\times n}$. How can I efficiently sample from $X | {\min{X}\le 0}$? (I.e. from the distribution of $X$ ...
0
votes
0answers
149 views

Hypothesis test for truncated distributed random variables in Bayesian Regression

As per the recommendation, I am re-framing my questions. I am doing a Bayesian Regression where the parameters are truncated at zero ($0< \beta < \infty$, Assuming prior to follow truncated ...
0
votes
0answers
242 views

Formular Derivation - Expected Value Truncated Normal Distribution [duplicate]

i want to derive the following expected value formular for $p(x)= N(\mu,\sigma^2)$ (see https://en.wikipedia.org/wiki/Truncated_normal_distribution): $$E[X|a<X<b]=\mu+\sigma\frac{\phi(\alpha)-\...
3
votes
0answers
70 views

Swiss Cheese Distributions

I am curious about a normal distribution with no probability mass in certain regions, sort of like the complement of the truncated normal. In particular, it will have zero mass in a circular region. ...
2
votes
1answer
788 views

Conditional distribution of a normal distribution given it is smaller/bigger than another normal distribution

Say I have two independent random variables $X \sim N(u_1, \sigma_1)$ and $Y \sim N(u_2, \sigma_2)$. I want to get the conditional distribution of X given whether X is bigger than Y or not. $P(X|X<...
1
vote
0answers
25 views

Interval of distribution is underrepresented in sample: Is there a way to estimate frequency in ground truth?

I heard about the concepts of censored and truncated data. Now I'm searching for the right concept to express something that is similar to truncated data: As far as I understood, in truncated data ...
0
votes
1answer
2k views

If a multivariate Gaussian distribution is truncated what will be the new distribution?

I have a covariance matrix and mean values(OMEGA) for a multidimensional Gaussian distribution (3-dim) as follows (respectively), ...
1
vote
0answers
150 views

Determining mean and SD of a parent normal distribution from a truncated data set

This seems like it should be easier than it is, but I'm stuck trying to determine if a data set I have represents a truncated normal distribution. The hypothesis I'm testing is that the data you see ...
1
vote
1answer
145 views

What is the name of this modified Gaussian?

I am reading a paper that defines $$ \mathcal{T}(x, \mu, \sigma) = A \cdot x \cdot \exp \left \{ - \left[ \frac{x-\mu}{\sigma} + \frac{\sigma}{2 \mu} \right]^2 \right \}.$$ It is introduced in ...
0
votes
0answers
202 views

Estimate truncation point of truncated normal given the mean and variance of the distribution

If we know the pre-truncated distribution follows the standard normal distribution and we know the post-truncated mean and variance, is it possible to calculate the truncated point of the truncated ...
2
votes
0answers
64 views

For $y=x+\epsilon$, how can we obtain the SD of $x$ when $y\gt t$

Given that $$ \begin{align} x&\sim N(0,\sigma^2=h^2)\\ \epsilon&\sim N(0, \sigma^2=(1-h^2))\\ y&=x+\epsilon \end{align} $$ Then $y$ is essentially a bivariate normal distribution with $\...
3
votes
1answer
321 views

How to analyze random variables with non normal distribution

I'm wondering how random variables can be analyzed using parametric methods if the distribution is not normal. For example if a variable Y is normal distributed but I'm interested only on values Y2 ...
1
vote
0answers
39 views

Support of sum of dependent truncated distributions

In case of independent truncated distributions, we can know the support of their sums from their convolutions. How about the dependent counterparts? In my case, I sum 9 dependent truncated ...
2
votes
1answer
180 views

How do you sample $\mathcal N(\mu, \sigma^2)$ from a range?

How can we generate a sample in the interval $[a,b]$ based on a Gaussian distribution? If we have a Gaussian random generator, just by mapping the number to the range and pruning (ignoring) the ...
2
votes
1answer
885 views

Sampling from Truncated Normal

I am trying to sample from a truncated normal using the standard probability integral transform as described on wikipedia with $$ x = \Phi^{-1} ( \Phi(\alpha) + U*( \Phi(\beta) - \Phi(\alpha)))*\sigma ...
0
votes
1answer
142 views

Generate data if parameters for population are known [duplicate]

I know the mean and standard deviation of a population, and its minimum and maximum value. How can I generate each data value from those parameters (using R) with the assumption that the data is ...
2
votes
0answers
265 views

Partly truncated and not truncated data

In some places 100 km races stop to count time if a certain time limit has been passed, for example 15 hours. It is difficult, respective, not possible to distinguish which finisher or site was ...
4
votes
2answers
746 views

Why is the output weights matrix initialized in a different way as the word embedding matrix in word2vec?

I was plagued by this problem while reading the tensorflow tutorial. There the word embedding is intialized as follows: ...
1
vote
1answer
4k views

Fitting truncated distributions using fitdistrplus with a lower bound of zero

I have been working to fit a normal distribution to data that is truncated to only be zero or greater. Given my data, which I have at the bottom, I previously used the following code: ...
12
votes
2answers
3k views

What is the benefit of the truncated normal distribution in initializing weights in a neural network?

When initializing connection weights in a feedforward neural network, it is important to initialize them randomly to avoid any symmetries that the learning algorithm would not be able to break. The ...
1
vote
1answer
667 views

Truncated Normal distribution: Theoretical mean outside truncation boundaries

I am working with a truncated normal as posterior distribution in a Bayesian estimation problem. Precisely, it is a normal distribution truncated at 0 from below. When calculating the parameters of ...
7
votes
1answer
542 views

Truncated normal distribution over a union of intervals

Suppose I want to find a truncated normal distribution, but instead of its being defined on an interval $(a,b)$, where $-\infty<a<b<\infty$, its definition is on an interval $(a,b)\cup(c,d)$, ...
1
vote
0answers
115 views

Finding moments of the untruncated distribution from the moments of the truncated one

I would like to get the moments of a normal distribution from the moments of a two-sided truncated normal distribution in R. Their formulas are available on the truncated normal distribution ...
0
votes
1answer
828 views

Truncated Gaussian distribution interpretation

What is the interpretation/logic of this formula: It's probability density function $f$, for $a<x<b$, is given by $$ f(x;\mu,\sigma^2,a,b) = P(x|a<x<b) = \frac{p(x, > a<x<...
1
vote
1answer
936 views

What is the difference between a truncated normal distribution and a half normal distribution in a Stochastic Frontier Analysis?

I am trying to replicate a SFA where the error term u is assumed to have a cumulative normal distribution function truncated from below at zero. In my opinion, that refers to a truncated normal ...
1
vote
0answers
574 views

Confidence Intervals of a one sided truncated normal distribution

Assume $y\sim N(\mu,\sigma^2)$ it can be shown that UMP alpha ($\alpha$) level tests are derived from the $\alpha/2$ quantiles i.e. $z(\alpha/2)$ How can we find confidence intervals of a truncated ...
0
votes
0answers
245 views

Normalization factor of truncated multivariate normal distributions (Normalization factor from samples)

I would like to evaluate an expectation of the form $\int p(x) \;\mathbb{1}_\left(Bx \leq 0\right) dx$, where p(x) is a multivariate normal distribution. I.e. the probability of a linear constraint ...
0
votes
1answer
676 views

Fitting a truncated normal distribution between 0 and 1 with a logit link function in R

I am modeling data that are proportions between 0 and 1, with many values of 0 and 1 in the data set. I'd like to model this as a truncated normal between 0-1, using a logit link in ...
2
votes
0answers
446 views

Truncated normal mean and CDF

Suppose $F(x;\mu,\sigma^2,0,1)$ is the CDF of a $N(\mu,\sigma^2)$ random variable $x$ truncated on the unit interval $(0,1)$. I'd like to show that $\frac{\partial}{\partial \mu} F(x;\mu,\sigma^2,0,1) ...