# Questions tagged [truncation]

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

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84 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 ...
19 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 ...
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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....
175 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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### 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 ...
17 views

### Appropriate censoring and truncation for customer survival analysis

I am working on a regular customer survival analysis problem. Here I analyze customers who signed up between 2015-1-1 & 2018-1-1. Customers can register anytime during this interval and exit ...
57 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 ...
34 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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### 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!
42 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). ...
25 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 ...
547 views

### 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 ...
84 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 ...
57 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 $\sigma$. ...
1k 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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### 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 ...
331 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 ...
32 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 ...
340 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 ...
153 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 ...
272 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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### 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 ...
900 views

### 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 ...
218 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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### 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 ...
422 views

### Weibull Regression of Left Truncated Data in R

I have a data set of tree diameters that do not include any measurements below a 7.5 due to the difficulty in identifying species when they are small. I want to run a Weibull regression that returns ...
353 views

### Definition of Zero-truncated Poisson distribution

The definition of zero-truncated Poisson (ZTP) distribution is: \begin{align} g(k;\lambda)= P(X = k | X > 0) &= \frac{f(k;\lambda)}{1-f(0;\lambda)} \\[8pt] &...
951 views

### Right-Truncated Survival Analysis

I'm working on a survival analysis in R using the survival package - and I am wondering what modifications I need to account for when using right-truncated data (which I think is what I have) (there ...
72 views

### 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. ...
375 views

### 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 ...
25 views

### 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 ...
2k views

### Efficiently sampling a thresholded Beta distribution

How should I efficiently sample from the following distribution? $$x \sim B(\alpha, \beta),\space x > k$$ If $k$ is not too big then rejection sampling may be the best approach, but I am not ...
519 views

### A truncated exponential distribution is surely not an exponential distriution?

I'm currently working through a set of old past exam papers for a course, and came across this question which just has me flummoxed. I've slightly rephrased the relevant information and the question ...
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### How to estimate parameters of a distribution with left-truncated and right-censored data?

I have been trying to find the best way of estimating parameters for a known pdf from a data-set that is left-truncated and right-censored. More precisely, I have lifetimes for a system where there ...
44 views

### 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?
125 views

### Why truncation intervals are refered as (a,b], (a,b), or [a,b]?

From the definition, the probability density function of truncated distribution is $$f_{a,b}(x) = \frac{f(x)}{F(b) - F(a)}$$ Now, the truncation interval is referred $(a, b]$, e.g. in Wikipedia, ...
638 views

### First and second moments of truncated laplace distribution

I'm trying to estimate a distribution that looks like a truncated Laplace distribution. However, I can't find closed-form expressions of its first and second moments. I'm expecting closed-form ones as ...
84 views

### Distribution function of an exponential random variable

I need to determine the distribution function of an exponential r.v. with mean 2, given that its outcome is larger than 2 and give the resulting expected value. I understand that the pdf is Given ...
202 views

### How do you sample $\mathcal N(\mu, \sigma^2)$ from a range?

How can we generate a sample in the interval $[a,b]$ based on a Gaussian distribution? If we have a Gaussian random generator, just by mapping the number to the range and pruning (ignoring) the ...
Suppose that I am working with an integer-valued variable $x$ and that all I know about my sample is as follows: Mean $\bar{x}$: 4.5 Sample size $n$: 100 I can safely assume that the underlying model ...