# Questions tagged [truncation]

Truncation is a process that results in the omission of data that are beyond a threshold.

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### How to deal with left truncation in cox model in R

I have a longitudinal data with 5 follow-ups. My aim is to see the effect of a disease on ability decline at old age. In my study, I have sibling pairs, one with disease (1) and one without disease (0)...
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### Expected value of a random variable with truncation

Let $f:[0,\infty)\to \mathbb R_+$ denote the PDF of a random variable $X$ and $c>0$ a constant. I want to evaluate the following integral: $$I(c)=\int_0^\infty{\min(x,c)f(x)dx}.$$ This can be ...
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### Distribution of a sample of uniformly distributed points in the 2D

Let there be a rectangle in the plane and a set of points distributed in the rectangle by a uniform distribution. I select a random point on the top and right border and draw the red line. The blue ...
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### DAGs and missingness/truncation

Being sort of new to the DAG way of thinking, I have a hard time wrapping my head around this question: What's the best way to represent the following problem as a DAG? Consider a simple regression ...
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### Converting untruncated Poisson regression effects to truncated effects - theory behind formulae

I am running a zero-truncated Poisson regression in R and the output provides untruncated mean lambdas for effects (i.e. includes values < 1). I have been advised to consider applying one of the ...
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### Hospital length of stay: change in the truncation value between years

I'm working on a paper estimating length of hospital stays for several years. Due to a change in the regulations the maximum time a hospital claim could remain open has changed in the middle of the ...
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### Dealing with left-, right- and interval-censoring and left- and right-truncation

I have a survival data set with left-, right- and interval-censoring and left- and right-truncation. Now I want to fit a Cox proportional hazard and an AFT model to these data. What is the best way to ...
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### How to use logistic regression with original values from a dependent variable that is a ratio?

I have a dependent variable that is a ratio, i.e. it takes the values between 0 and 1. Some 30% of values are 1s. The dependent variable measures the distribution of funds, i.e. it is calculated just ...
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### Why is it problematic to use OLS for a bounded dependent variable (e.g. a ratio variable)?

I have a question that emerged from my previous post. If you look at my previous post, the dependent variable there is a ratio variable and thus is bounded, i.e. it can only take the values between 0 ...
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### Flawed multiple linear regression in academia? Heteroscedasticity's effect on p-value?

I believe I have found a paper in academia that has used a flawed multiple linear regression. I have downloaded the data set and replicated their regression results. I have done some diagnostics and ...
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### truncation of bivariate normal under quadratic condition

Consider a complex normal variable $Z \sim \mathcal{CN}(\mu,2\sigma^2)$ with real component $X \sim \mathcal{N}(\mu,\sigma^2)$ and imaginary component $Y \sim \mathcal{N}(0,\sigma^2)$. We can write ...
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### Bivariate normal and truncated expectation [duplicate]

What is the expectation $$\mathbb E[X_1 \lvert X_1 > X_2]$$ assuming that $$(X_1,X_2) \sim \mathcal MVN(0,\Sigma),$$ with $\mathcal{MVN}$ being the multivarite normal. I would expect this to have ...
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### Central Limit Theorem for Truncated observations

Consider a random variable $X$ with values in $\left[0,\infty\right)$ such that $E\left[X\right]=\infty$. Given $M > 0$ I want to estimate the expected value of $X$ truncated at $M$. That is I want ...
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### Truncating variable in survival analysis

this is my first time developing a survival analysis model so bare with me if the nomenclature is not on point. Basically, I'm running a Cox PH model for the length a contract is active, where 1 is ...
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### Partially left truncated data in bivariate time series, one series is missing data what to do?

I have two time series of futures Settlement Prices where I am to model the systematic volatility of the settlement prices for these two time series. My plan is to: Calculate the logged returns. Fit ...
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### Truncation based on two variables

I have some data, which has been constructed from multiple API pulls. Observations have an expiry date, $x_i$, which means that observations which expire before the API pull is done do not appear in ...
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### 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 ...
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### Understanding left-truncated data in survival analysis

I am having a hard time grasping the concept of left truncation. According to what I understand, left truncation occurs when we observe individuals only if their event of interest takes place after ...
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### How do we obtain the probability density of a truncated regression with an upper and lower bound

I know my density for $y$ is supposed to be something of this form $$g(y|x_{i},t)=\frac{f(y|x'\beta, \sigma^{2})}{F(t|x' \beta' \sigma^{2}}$$ where the numerator is the density of the normal ...
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### How to handle truncated or missing ranking data in a classification problem?

I'm preparing data for a classification problem that involves matches in a single-player sport. In each match, each competitor is either ranked and thus has a numeric rank; or unranked (rare but can ...
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### Moments of truncated Student's $t$-distribution

I performed random sampling on a Student's $t$-distribution. I used SciPy to calibrate my parameters and then truncated my allowable values to the maximum and minimum observation in the data for ...
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### Truncation versus censoring with Kaplan-Meier

I am trying to run Kaplan-Meier on a rather odd dataset and am having difficulty determining whether I should be truncating or censoring my data. I have looked at the other feeds, including this very ...
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### Fitting a gamma distribution to truncated data

I am faced with the following truncation problem: $$X_i \sim \Gamma(\alpha, \beta) \\ \delta_i = \chi(X_i \le \tau_i)$$ I can observe only $(X_i, \tau_i)$ where $\delta_i = 1$ and I have no a-...
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### What is a sensible way to truncate data to a region that fits a model?

I want to use an exponential decay model in python to relate the flow rate in a device to the mass left inside it, in particular $flow=a−b×e^{−c×mass}$ where a, b and c are the parameters of the model....
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### Distributions with simple truncated expectations

For a project I'm looking for continuous distributions which have a somewhat simple closed form for upper-truncation expectation ($E[x|x>c]$). Here are two examples I've found so far: Exponential ...
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### Truncation of distance matrix

Given a sample $\textbf{X}_1$,...,$\textbf{X}_n\in\mathbb{R}^p$ from an arbitrary distribution with distribution function $F$ we can calculate the pairwise Mahalanobis distances between the sample ...
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### How do to deal with data missing NOT at random?

It seems that because values are missing from a specific range of my target variable, my model performs poorly when predicting samples that are actually in that range. My target variable is ...
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### Estimate population variance / mean from truncated distribution with known cutoff, but without parametric assumptions

Suppose you have a sample of $N$ iid random variables $X_i$ drawn from an unknown (but finite variance) distribution but with a known upper-cutoff $K$ and therefore support $[0,1,2,...,K]$ but un-...
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### Right truncation and right censoring

Is is possible for a survival data to be **right truncated and right censored **. If so, please leave an example for better understanding. Thanks in advance!
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### Right censored or right truncation and Cox model?

Suppose, a list of targeted population is invited to participate in a health program. Invitation date could vary for every individual based on eligible criteria (this criterion is the same for all). ...
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### Can sampling from a truncation of a random variable, rather than the original variable be more Blackwell-informative?

Suppose you are interested in finding the mean of a random variable. You have some prior belief of it and before sampling 1 observation, you can decide whether to sample from the original random ...
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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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### Survival analysis: how to account for immortal time with time-dependent exposure

I am working on a survival analysis to look at time to preterm birth (birth before 37 weeks). I have a time-dependent exposure that can occur anytime at or after 28 weeks, defined using a heaviside ...
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### Working out the true mean of a distribution from a truncated set of observations

Suppose people receive a random draw which represents the probability of some event. The draws are taken randomly from a normal distribution with true mean $\mu$ and standard deviation $\sigma$. ...
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### Distribution of sum of independent exponentials with random number of summands

Let $\tau_i\sim\exp\left(\lambda\right)$ be independent and identically distributed exponentials with parameter $\lambda$. Then, for given $n$, the sum of these values $$T_n := \sum_{i=0}^n \tau_i$$ ...
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### Truncated count model -- including information about the number of unobserved realisations

Background Suppose we have a model such that $Y \sim \mathcal{M}(\theta)$ is a discrete random variable taking values in $[0, 1, \ldots]$. We would like to make inference about $\theta$ from a ...
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### Efficient random generation from truncated Laplace distribution

We have several ways of drawing random samples from Laplace distribution. Is there any efficient way of sampling from left truncated Laplace distribution? Inverse transform sampling is an obvious ...
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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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### How to model left-censored and right-truncated data on Stata? [closed]

I have data that is left-censored and right-truncated. I'd like to run a tobit or truncreg. Although, using ...
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### Survival in two period game: mean of z|z<v with z=xy, x~U(a,b) and y~U(c,d)

I am looking for the functional form to describe the following: A random shock $x\sim Uniform(a,b)$ is multiplied with a second shock $y\sim Uniform(c,d)$. What is the mean value of all combined ...
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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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### What does a truncated distribution mean? [duplicate]

I am a little bit confused about truncated distributions such as truncated normal distribution. I have a code in FORTRAN where the function gen_rnorm(mean,sigma) ...
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I have a particular situation. I would like to build a probit model to predict a given outcome $Y=\{0,1\}$ based on a set of predictors $X$. A probit model has the form: \text{Pr}(Y=1\,|\,X)=\Phi(...