Questions tagged [truncated-normal]

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

Filter by
Sorted by
Tagged with
0
votes
0answers
4 views

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: ...
2
votes
1answer
37 views

Probability of standard normal greater than another standard normal conditional on truncation

$X,Y \sim N(0,1)$ independently. Find $P(Y > 3X | Y > 0)$. My attempt: $$\begin{eqnarray*} P(Y > 3X | Y > 0) &=& P(X < Y/3 | Y > 0) \\ &=& E(1(X < Y/3)| Y > 0) ...
0
votes
1answer
62 views

Truncated normal distribution without scaling

My understanding of a truncated normal distribution $\mathcal{N}(\mu,\sigma;a,b)$ is that it results from scaling the values of a normal distribution within the bounds $[a; b]$ such that the area ...
0
votes
0answers
7 views

Valid to truncate KF state estimate?

In the field I study I have come across several cases where the Kalman Filter is used together with truncating the state estimate. The most recent case is a study where the algorithm cuts the ...
1
vote
2answers
37 views

Compute Mean of a Clipped Normal Distribution

I am trying to solve this problem and have solved all parts except for the last part. I have tried to research the problem and saw some theory on truncated normal distributions and found this formula ...
2
votes
0answers
15 views

Is it Sufficient to Truncate a Left Censored Distribution?

A colleague explained their approach to dealing with left censored data in an analysis, and while I don't think it is the best approach, I am not sure if it is insufficient or not. My colleague has ...
1
vote
0answers
40 views

autocorrelation for truncated normal distribution

I have a (symmetric) truncated normal distribution from which I'm sampling. There is also auto-correlation of the values, so I know: $\mu, \sigma,$ autocorr = $a$ All three of these values are single-...
3
votes
1answer
913 views

Expected value of X^3 for a normal distribution given it has limits?

What is the expected value of $X^3$ with in limits for a normal distribution? In other words, I am looking for solution of $E(X^3 \mid a\leq X \leq b)$.
5
votes
1answer
57 views

Average of the outside of a truncated normal distribution

I have a sample that is normally distributed ~ $N(\mu,\sigma)$ and truncated between $a,b$ such that $a<b$. I saw a Wikipedia article that the average of the truncated part is $\mu + \frac{\phi(\...
1
vote
1answer
27 views

Truncated CEF of normally distributed RV. Is sample analogue a consistent estimator of the 'population' truncated CEF?

If I have a random variable that is normally distributed, and truncated such that I only see $y$ if $y\geq 0$, and I want to do some calculations with the truncated Conditional Expectation Function in ...
1
vote
1answer
24 views

How to derive the distribution of a Random variable which is a function of Normal

I am interested to know the distribution of following expression - X ~ N(0, 200) Y = min(X + c, 0), c > 0 I thought Y ...
-1
votes
1answer
107 views

How to fit a mixture of a normal and a half normal distribution?

I tried Expectation-Maximization (EM) based fitting using the mixfit function from the mixR package in the R environment. It yielded a normal mixture model with 2 components: 1) pi 0.21, mu: 0.47, sd: ...
0
votes
0answers
30 views

Interpreting truncated normal and lognormal coefficients

I am running a truncated normal regression and a lognormal regression as the second part of a double hurdle model. The dependent variable is transaction revenue and I have several independent ...
2
votes
1answer
38 views

truncated model estimation, on an interval of unobserved variable Y*

$Pr[L<Y^*<U]=Pr[Y^*<U]-Pr[Y^*<L]$ $=F^*(U)-F^*(L)$ $lnL_n(\theta)=\sum_{i=1}^nd_iln[F^*(U|x_i,\theta)-F^*(L|x_i,\theta)]$ ^is the above likelihood function appropriate for ...
0
votes
0answers
73 views

Mean and variance of conditional distribution of truncated normal distribution

Let's say that I have $$\begin{pmatrix} x \\ y \end{pmatrix} \sim N \begin{pmatrix} \begin{pmatrix} \hat{x} \\ \hat{y} \end{pmatrix}, \begin{pmatrix} A & C \\ C^{T} & B \end{pmatrix} \...
1
vote
1answer
56 views

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 ...
1
vote
1answer
32 views

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 ...
1
vote
0answers
38 views

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 ...
1
vote
1answer
343 views

Uniform Prior on Normal Mean with Known Variance Implies Truncated Normal Posterior?

Let's say I have a uniform prior $\mu \sim \mathcal{U}(a,b)$, a normal likelihood $y|\mu \sim \mathcal{N}(\mu,\sigma^2)$ with known variance $\sigma^2$, and one observation $y$. Is then the posterior $...
2
votes
1answer
83 views

What is E[X|X+Y < z] with X, Y independent Normals?

Let $X\sim N(\mu_X,\sigma_X^2)$ and $Y\sim N(\mu_Y,\sigma_Y^2)$ and $Cov(X,Y)=\sigma_{XY}$. Define $Z=X+Y$. I know that $E[X|Z=z]=\mu_X + \frac{\sigma_X^2+\sigma_{XY}}{\sigma_X^2+2\sigma_{XY}+\...
4
votes
1answer
77 views

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 ...
4
votes
0answers
38 views

Integration by sampling from truncated distribution

I'm reading the book Ben Lambert's Bayesian Statistics: problems and answers, which by the way I like. There is a group of problems in "Integration by Sampling" chapter 12. The first integral is $$...
0
votes
0answers
38 views

Integral and expected value for multivariate distribution

for the last couple of days I have been struggling with a problem and I was hoping to get some help here. I have a function that looks as follows: $$ f(x,y,z)=\begin{cases} 0 & \text{if} \ (x*...
1
vote
1answer
40 views

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 ...
0
votes
1answer
43 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 ...
6
votes
2answers
1k 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
408 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
548 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. ...
2
votes
1answer
76 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 ...
5
votes
0answers
195 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
38 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
46 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 ...
1
vote
1answer
322 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 ...
6
votes
2answers
225 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
2k 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
35 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
435 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
499 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
319 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
245 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 ...
1
vote
0answers
225 views

Linear combination of truncated normals

I am trying to calculate the following expression: $$ Z = \mathbb{E}\left[\left| \langle \mathbf{a}, u \rangle \right| \right] = \left| \sum_{i=1}^d a_i u_i \right|, \quad \left\| u \right\| = 1 $$ ...
3
votes
2answers
107 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.)
3
votes
1answer
646 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
130 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
312 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
267 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
78 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
2k 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
3k 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), ...