Questions tagged [truncation]
Truncation is a process that results in the omission of data that are beyond a threshold.
49 questions with no upvoted or accepted answers
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The marginals of a truncated multinomial are truncated binomials?
The multinomial distribution for a vector $\vec x$ of non-negative integers assigns a probability of:
$$f(\vec x) = n!\prod_i p_i^{x_i}/x_i!$$
to every vector $\vec x$ of non-negative integers in ...
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Truncated response variable in boosted regression trees
I was thinking about the differences in approaches between parametric and non-parametric statistics in regression.
I am working with a non-negative integer response $N\in\mathbb{N}_{0}$.
Let's imagine ...
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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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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.
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Unbiased Estimator of the truncation points in a truncated normal distribution?
Consider the variables $x_i \sim \mathcal{N}(\mu, \sigma^2,a,b)$ iid with truncation points $a$ and $b$, i.e. $a < x_i < b$.
Suppose all four parameters, namely $\mu, \sigma, a, b$ are unknown.
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Two-part models in R: continuous outcome with too many zeros
I am estimating a model where the outcome variable is continuous, more specifically a percentage in the form of a 0 to 1 range. This variable has one potential problem: many of its cases equal zero (...
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Finite mixture models with bounded data
I am trying to fit a finite mixture model to a dependent variable which is bounded (practically) between -0.594 and 1 (theoretically, the latent variable is bounded between -Inf - 1). The data are ...
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Estimating parameters in a truncated negative binomial distribution?
I would like to find the estimates of the parameters in a truncated (at zero) negative binomial distribution. Suppose $Z$ has this distribution with parameters ($\alpha,\beta$). (The parametrization ...
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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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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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Why is this Bayesian estimate of a truncation-point so poor?
I have several datasets. Each dataset holds the masses of objects that have been subject to physical wear, expressed as a proportion of their original mass ($w$), and the amount of time that the ...
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Is there a way to model left truncated and interval censored data in R or SAS?
We have a study where our participant underwent some surgery at time = 0, but at various ages. Our follow-up is based only on Medicare age-eligible people, so we have to wait until they reach the age ...
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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 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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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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List Experiments as Right-Truncated Poisson?
A common scenario for the analysis of list experiments:
Note: the standard list experiment is also known as the Item Count Technique (see Imai 2011: http://imai.princeton.edu/research/list.html)
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Conditional moments of bivariate normal
Suppose that (X,Y) are bivariate normal with non-zero means and correlation. Is there any neat expression for $\mathbb{E}(X|Y>0)$?
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Proving a "well-known" result regarding the distribution of a normally distributed random variable
In an important project work, I would like to include a "proof" of the following, but have unfortunately been unable to readily compute it myself. I am aware that this is a flaw on my part, but ...
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proper one-sided test for truncated distribution
I have positional segments that contain N number of mutations. Each mutation has a frequency which is determined by taking the number of reads supporting the alternate allele (r) and dividing them by ...
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Truncated normal in WinBUGS
I want to use the following truncated normal distribution in WinBUGS to estimate parameters of SEM using Bayesian analysis.
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Where can I get reference formulas for truncated distributions?
I have been comparing tails of various distributions for an application where we will need the conditional expectation of the tail or a truncated tail:
$E(X | a<X \leq b )= \frac{\int_a^b x f(x) ...
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560
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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 ...
user359974
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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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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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1
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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_{...
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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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163
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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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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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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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557
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Do I have Left Truncation or Right Censoring in my Survival/Event History Analysis?
I am doing study that starts at a specific date, January 1st 2015, and ends on a specific date, December 31st 2015. My overarching research question revolves around modeling time between orders of ...
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Sampling from a truncated random effects distribution
How would one sample observations $T_{ij} = U_i + \varepsilon_{ij}$, where the distribution of $U_i, \varepsilon_{ij}$ are known and mutually independent, condition on the fact that $L_{ij} \le T_{ij} ...
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Does deleting right censoring data make it to be left truncated?
If data have right censoring and complete data, I delete the right censored ones. Does it make the data to be left truncated? And why?
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Estimating Gamma MLE with left truncated data (using R and maxLik)
I'm trying to find the maximum likelihood estimation of the parameters of a Gamma distributed random variable using maxLik.
The following code explain what I did:
...
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Truncated distribution $f(x;\theta)=\theta x^{-(\theta-1)}$
I'm trying to derive for p.m.f.
$$f(x;\theta)=\theta x^{-(\theta-1)}$$
$x>1, \theta > 0$
the truncated distribution that excludes observations $1<X≤a$
$$f(x | X > a)=\frac{g(x)}{1-F(a)}$...
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461
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Regression with dependent variable which ranges from -1 to 1
I performed a series of Pearson correlations which give me as expected values between -1 and 1 (actually very few below zero). I'd like now to see if some factors are linked to these correlation ...
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error on truncated rms
I am computing the RMS of a sample to estimate the standar error $\sigma$ of the underlying distribution (for simplicity let say a normal distribution $N[\mu$, $\sigma$]).
$ \text{RMS} = \sum_{i=1}^N ...
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Is it possible to model BOTH censoring and truncation in BUGS?
Survival times are often right censored and left truncated. From my experience, it does not seem like OpenBUGS allows for both. Truncation is denoted as T( , ) and censoring as C( ,).
For instance, a ...
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Which log-likelihood is to be maximized for left-truncated count data?
What is to be done, if the count data is missing the counts on the zeros (i.e. left truncated data)? Say one wants to estimate a Poisson regression and the goal is to derive the log-likelihood to be ...
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Estimating a censored distribution curve
I have a sample of only 142 numbers from a distribution of 3852 numbers ranging from 0 to 53, but it is censored below 35 (The values exist, but I don't have access.), so I have only the values in ...
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How to model an uncertain (or erroneous) truncation effect on a random variable?
Let $ V_a $ be a random variable which is truncated at a value $v_c$. Therefore, the updated density function of truncated $V_a$ is given by,
$$ f(v_a| V_a\leq v_c) = \frac{g(v_a)}{F(v_c)}$$
where $g(...
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Expected value of a random variable with truncation
Let $f:[0,\infty)\to \mathbb R_+$ denote the PDF of a random variable $X$ and $c>0$ a constant. I want to evaluate the following integral:
$$I(c)=\int_0^\infty{\min(x,c)f(x)dx}.$$
This can be ...
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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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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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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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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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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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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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1
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Would there exist a symmetry around the mode in a truncated uni-modal distribution (which is differentiable)?
If we truncated around the mode of an asymmetric (continuous and differentiable) unimodal distribution, would there be a symmetry around the truncation point?
For example if X is generated from an ...
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