Questions tagged [truncation]
Truncation is a process that results in the omission of data that are beyond a threshold.
123
questions
2
votes
2answers
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 ...
0
votes
0answers
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 ...
2
votes
1answer
36 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-...
2
votes
1answer
32 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....
4
votes
2answers
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 ...
0
votes
0answers
24 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 ...
0
votes
0answers
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 ...
3
votes
1answer
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 ...
1
vote
0answers
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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votes
0answers
34 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!
0
votes
0answers
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). ...
1
vote
1answer
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 ...
5
votes
1answer
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 ...
1
vote
0answers
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 ...
0
votes
0answers
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 $\sigma$.
...
asked Mar 14 '19 at 6:37
user1205901 - Reinstate Monica
9,02716 gold badges63 silver badges119 bronze badges
7
votes
1answer
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
$$T_n := \sum_{i=0}^n \tau_i$$
...
1
vote
0answers
41 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 ...
6
votes
2answers
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 ...
1
vote
0answers
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 ...
-1
votes
1answer
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 ...
1
vote
2answers
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 ...
2
votes
0answers
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 ...
0
votes
0answers
52 views
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) ...
3
votes
1answer
298 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:
$$\text{Pr}(Y=1\,|\,X)=\Phi(...
5
votes
2answers
808 views
Mean vs. Trimmed mean in the normal distribution
In a simple experiment with the normal distribution in R I ran 500 iterations of a simulated normal distribution with N=100 each. For each iteration from the 500 iterations, I calculated both the ...
1
vote
0answers
84 views
Right, Left, Interval, Delayed, and truncted data
I have a medical data set that has all the following cases:
Right-censored
Left-censored
...
3
votes
1answer
146 views
Expectation of $X$ given $X < c$
Let $X$ be a random variable with PDF $f(\cdot)$ and CDF $\Phi(\cdot)$. I want to compute $E(X \mid X < c)$, where $c$ is some constant.
Using definition of the expected value
$$E(X \mid X < ...
2
votes
1answer
479 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 ...
7
votes
1answer
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 ...
0
votes
0answers
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 ...
1
vote
1answer
80 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 ...
0
votes
1answer
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 ...
2
votes
1answer
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]
&...
3
votes
3answers
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 ...
3
votes
0answers
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.
...
1
vote
0answers
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 ...
-1
votes
1answer
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 ...
10
votes
2answers
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 ...
3
votes
1answer
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 ...
8
votes
3answers
2k views
PDF of sum of truncated exponential distribution
Let $x_i$ represent samples from a Truncated Exponential distribution between $0$ and $1$, with rate parameter $\lambda$.
Defining
$\tilde x = \dfrac{\sum_{i=1}^{n}x_i}{n}$
What is the PDF of $\...
7
votes
2answers
512 views
How to compare clinical trial data to a natural history control
Context: I am interested in understanding how to analyze data from clinical trials with a natural history control, meaning, a clinical trial where a group of people (say, those with genetic risk for a ...
1
vote
0answers
28 views
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} ...
3
votes
1answer
610 views
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 ...
1
vote
0answers
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?
2
votes
1answer
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, ...
2
votes
2answers
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 ...
1
vote
1answer
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 ...
2
votes
1answer
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 ...
0
votes
1answer
240 views
Regression on leptokurtotic data
I'd like to model some data with high kurtosis, with the goal of predicting the response variable outside some threshold in the tails especially.
OLS seems to do a bad job of this as the residuals ...
2
votes
1answer
503 views
Bayesian estimate of the parameter of a truncated Poisson distribution (using R)
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 ...
