# Questions tagged [truncated-normal]

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

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### Input Covariates vs. Inefficiency Covariates in a Stochastic Frontier Analysis of Student Grades

I'm modeling student exam and course grades (very left-skewed as expected) using a stochastic frontier model with a truncated-normal inefficiency term (in Stata: ...
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### Implementing a truncated regression for a normal distribution in R

I'm not a statistician but I'm working with some experimental psychology data. I have a distribution of responses on a -4 to 4 scale. Usually, these type of variables is treated as continuous. I have ...
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### How do I find the standard deviation that results in a specific probability coverage in a truncated normal distribution?

Given a truncated normal distribution $X$ with mean $\mu$, lower limit $a$, and upper limit $b$. How can I pick a standard deviation $\sigma$ such that $P(\mu -x\leq X \leq \mu+x)=y$ for some ...
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### Precision issues using truncnorm in R [closed]

I'm facing some precision issues with truncnorm, particularly the ptruncnorm() function in R. Here's an example where I find the cdf up to $q= 2$, where the truncation point is $1.9$, for several ...
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### How do I calculate $s$ from $\mathbb P(X+Y>u\mid X<s)=q$

Suppose $X,Y$ are (not necessarily independently) normally distributed, how can one calculate the maximal limit $s$ that $X$ may reach such that the probability of the sum $X+Y$ overshooting a given ...
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### d to r conversion for extremely high versus extremely low groups

Context Suppose I am performing a meta-analysis on the relationship between two variables (say depression and life satisfaction). Unfortunately, many studies in the prior literature do not report ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 $\mathrm E(x\mid y>0)$ ?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Linear combination of truncated normals

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