# Questions tagged [truncation]

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

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### Which log-likelihood is to be maximized for left-truncated count data?

What is to be done, if the count data is missing the counts on the zeros (i.e. left truncated data)? Say one wants to estimate a Poisson regression and the goal is to derive the log-likelihood to be ...
1 vote
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### Survival analysis when event cannot happen after timepoint

People are contacted for a survey for a fixed number of days. For simplicity, let's say this happens over 5 days. People can complete their survey on day 1, day 2, ..., up to the end of day 5. After ...
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### Prediction metrics for left-truncated and right-censored data

I am trying to assess (out-of-sample) predictive performance of survival analysis models with left-truncated and right-censored data. Assume the training and test data, respectively, consist of ...
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### Formula for standard deviation of a normal distribution from truncated data [closed]

I have some samples taken from a normal distribution of unknown $\mu$ and $\sigma$, and I know someone took away the top and bottom $p$ percent of the original samples ($p$ is known). Is there a ...
1 vote
2k views

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

I have a longitudinal data with 8 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 ...
• 113
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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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### 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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1 vote
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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 ...
• 351
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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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1 vote
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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 ...
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 ...