Questions tagged [truncation]

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

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Can I estimate the mean of a dataset if I have its standard deviation and a portion of the full data that is higher than some threshold?

I have a partial set of measurement data that is limited due to my tool's sensitivity. I know that the data is approximately normally distributed and I have a standard deviation from another data set ...
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Left Truncated Data survival data

I am working with a data that is I believe left truncated. I am looking at how Veterans with MPNs have a different timing of arterial thrombosis (AT) compared with Civilians with MPNs. In the data ...
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On the difference of truncated Gaussian and a new definition

Given a r.v. $X \sim N(0, 1)$, what is the density of $Z = X I(\lvert x \rvert < \lambda)$. I am confused with the truncated Gaussian $Y = X$ if $\lvert X \rvert < \lambda$ otherwise $Y = 0$. My ...
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Derivation of Truncated Derivatives in Hochreiter's original LSTM Paper

I was trying to understand the derivation of the truncated derivatives in Hochreiter's origin LSTM paper. Spent a bunch of time without avail. I suppose I am missing a way to map my intuition of ...
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Difference between conditional survival and left truncation analysis for cancer patients?

I am looking at cancer patient survival and want to know how long-term survival is after already having survived some time. I am more familiar with conventional conditional survival, but have recently ...
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Estimating a censored distribution curve

I have a sample of only 142 numbers from a distribution of 3852 numbers ranging from 0 to 53, but it is censored below 35 (The values ​​exist, but I don't have access.), so I have only the values in ...
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Distribution closed under convolution and truncation followed by convolution

Let $D(\theta)$ denote an absolutely continuous distribution on $\mathbb{R}$. (The finite dimensional vector $\theta$ collects the parameters of the distribution.) Assume that the p.d.f. of $D(\theta)$...
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Left truncation or left censoring?

I am conducting a study in which I analyse the time to opt out after the free trial is ending. I have individuals who sign up for a free membership-trial period. At some point the period is ending and ...
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Likelihood contribution of censored data - why conditional?

Let $x_i$ be a sample of survival time from right-truncated data with right-truncation time $Y_R$. I would like to find the likelihood contribution from the sample. I thought I have to find the ...
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Parameter estimation on exponential distribution from a bounded subset of that distribution

I have a random variable that is exponentially distributed with some $\lambda$. I'm sampling observations from this variable, but I'm limited to observing only those that are less than some maximum ...
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Distribution of a constrained Gaussian distribution in frequency domain

We know that a Gaussian Distribution is not limited and it spans from $-\infty$ to $+\infty$ . However, practically if we sample the Gaussian with a finite sampling frequency, the maximum frequency is ...
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Is my data right censored or right truncated?

I have a dataset of the percent of pavement area that is cracked and time as the explanatory variable for a city's streets. Engineering principles and logic tell us that as that as time progresses, ...
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How to model an uncertain (or erroneous) truncation effect on a random variable?

Let $ V_a $ be a random variable which is truncated at a value $v_c$. Therefore, the updated density function of truncated $V_a$ is given by, $$ f(v_a| V_a\leq v_c) = \frac{g(v_a)}{F(v_c)}$$ where $g(...
Shihab Khan's user avatar
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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 ...
relatively_random's user avatar
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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 ...
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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 ...
M a m a D's user avatar
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Simulation of a truncated normal distribution over two intervals

Given $X$ a random variable with a normal distribution, what is the best procedure to simulate $X|X\in[a;b]\cup[c;d]$, i.e. we want to simulate the truncated normal distribution only on the intervals $...
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Better understanding of censoring and truncation (in particular right truncation) in survival analysis

I am taking a course in survival analysis where we follow the book "Survival Analysis: Techniques for Censored and Truncated Data" by John P. Klein and Melvin L. Moeschberger. Although I ...
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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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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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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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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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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_{...
andrjens's user avatar
4 votes
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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 ...
Tino's user avatar
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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 ...
Ken Lee's user avatar
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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 ...
Ken Lee's user avatar
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4 votes
0 answers
117 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 ...
Jesper for President's user avatar
3 votes
1 answer
394 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 ...
steveo'america's user avatar
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1 answer
115 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 ...
amestrian's user avatar
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1 answer
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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 ...
Jens Kramer's user avatar
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22 views

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 ...
Oska Fentem's user avatar
2 votes
0 answers
56 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 ...
Dave Bapst's user avatar
5 votes
1 answer
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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 ...
Alex's user avatar
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1 vote
1 answer
217 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 ...
yurnero's user avatar
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3 votes
2 answers
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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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160 views

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 ...
Janth's user avatar
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4 votes
1 answer
641 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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2 votes
1 answer
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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....
st210's user avatar
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4 votes
2 answers
439 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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124 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 ...
Ricsi Nincs's user avatar
2 votes
1 answer
191 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 ...
George's user avatar
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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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1k 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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165 views

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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