Questions tagged [truncation]

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

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58 views

Is it possible to calculate or find out what the original distribution was of a dataset? [duplicate]

Is it possible to calculate or find out what the original distribution was of a dataset? For example: I have (part of) a dataset with 800 weights and I know that the original dataset contained 1000 ...
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1answer
36 views

What is the correlation of a truncated bivariate Normal distribution?

$X$ and $Y$ are independent standard normal variables. If we generate $n$ samples $(x,y),$ what is the correlation for samples $(x, y)$ with $x+y\gt0$?
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27 views

Is trial with accrual period left truncated?

I am reading Dirk Moore's Applied Survival Analysis 11.2. "...However, patients actually enter over an accrual period of length a, and then, after accrual to the trial has ended, they are ...
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1answer
36 views

Censoring, truncated and missing data in Survival Analysis

Can someone please explain the difference between censored, truncated and missing data in survival analysis? Suppose I have following information. ...
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1answer
22 views

Baseline adjustment when both pre- and post values are subject to left-censoring

Assume $X$ is a binary treatment variable, $Y$ is a continuous variable measured pre- and post-treatment $(Y_{pre}$, $Y_{post})$, and $Z$ represents the remaining covariates. Both $Y_{pre}$ and $Y_{...
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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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1answer
142 views

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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1answer
38 views

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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1answer
108 views

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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1answer
174 views

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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101 views

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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1answer
97 views

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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1answer
41 views

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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1answer
19 views

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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1answer
282 views

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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1answer
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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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1answer
63 views

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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2answers
266 views

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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1answer
290 views

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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1answer
53 views

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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254 views

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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54 views

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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1answer
84 views

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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66 views

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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379 views

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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1answer
34 views

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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1answer
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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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91 views

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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87 views

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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1answer
3k views

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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42 views

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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538 views

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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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 ...
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1answer
491 views

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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2answers
337 views

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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435 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 ...
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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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1answer
480 views

Truncated probit regression

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(...
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2answers
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Mean vs. Trimmed mean in the normal distribution

In a simple experiment with the normal distribution in R I ran 500 iterations of a simulated normal distribution with N=100 each. For each iteration from the 500 iterations, I calculated both the ...
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1answer
118 views

Right, Left, Interval, Delayed, and truncted data

I have a medical data set that has all the following cases: Right-censored Left-censored ...
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1answer
648 views

Expectation of $X$ given $X < c$

Let $X$ be a random variable with PDF $f(\cdot)$ and CDF $\Phi(\cdot)$. I want to compute $E(X \mid X < c)$, where $c$ is some constant. Using definition of the expected value $$E(X \mid X < ...
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1answer
1k views

Poisson distribution where x is at least 1

Is this as simple as saying that the probability that x equals zero is $e^{-λ}$, so the probability that x is 1,2,..... is $1-e^{-λ}$, so we just divide the usual pmf for poisson distribution by the ...
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How to calculate a partial expected value of beta distribution (mean of a truncated beta)?

Given a Beta Distribution with a=2, b=3, we can find an expected value (mean) for the interval [0, 1] = a/(a+b) = 2/5 = 0.4 and median = (a - 1/3)/(a+b-2/3) = 0.39, which are close. I am looking for a ...
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397 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 ...
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1answer
148 views

Modeling potentially unimodal data

My data: I surveyed for animal densities across an elevation gradient. Let's say I surveyed from 0 to 1000 meters elevation. My models (one for each species of interest): density ~ elevation + other ...