Questions tagged [truncation]
Truncation is a process that results in the omission of data that are beyond a threshold.
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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 ...
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1answer
61 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 ...
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0answers
75 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 ...
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42 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 $\sigma$.
...
7
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1answer
542 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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0answers
33 views
Goodness of fit for zero truncated negative binomial model
I have calculated a zero-truncated negative-binomial model using glmmadmb, and also vglm, in R. I need to report some measure of goodness of fit for this model. I have already done cross validation (...
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37 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 ...
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17 views
Conditional expectation of RVs under truncation-based stochastic signal release?
Suppose $z\sim N(0,1)$ and $x\sim N(\gamma z, 1)$, where $\gamma$ is a known sensitivity parameter. That is, $x=z+\epsilon, \epsilon \sim N(0,1)$ where $\epsilon$ is exogenous.
Further, suppose there'...
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2answers
284 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 ...
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0answers
29 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 ...
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1answer
247 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 ...
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2answers
126 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 ...
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0answers
159 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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0answers
43 views
What does a truncated distribution mean? [duplicate]
I am sorry if this is a stupid question but I am little bit confused about truncated distributions such as truncated normal distribution. I have a code in FORTRAN where the function ...
2
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1answer
220 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:
$$\text{Pr}(Y=1\,|\,X)=\Phi(...
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2answers
692 views
Mean vs. Trimmed mean in the normal distribution
In a simple experiment with the normal distribution in R I ran 500 iterations of a simulated normal distribution with N=100 each. For each iteration from the 500 iterations, I calculated both the ...
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0answers
77 views
Right, Left, Interval, Delayed, and truncted data
I have a medical data set that has all the following cases:
Right-censored
Left-censored
...
3
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1answer
129 views
Expectation of $X$ given $X < c$
Let $X$ be a random variable with PDF $f(\cdot)$ and CDF $\Phi(\cdot)$. I want to compute $E(X \mid X < c)$, where $c$ is some constant.
Using definition of the expected value
$$E(X \mid X < ...
2
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1answer
287 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 ...
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1answer
689 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 ...
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0answers
148 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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1answer
67 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 ...
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1answer
320 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
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1answer
219 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]
&...
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3answers
761 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 ...
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0answers
70 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.
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0answers
311 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 ...
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0answers
13 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 ...
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2answers
1k 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 ...
4
votes
1answer
420 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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2answers
1k 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 $\...
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1answer
133 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 ...
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0answers
25 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} ...
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1answer
539 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 ...
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0answers
106 views
fitting right truncated weibull distribution [duplicate]
I am fitting a right truncated weibull distribution to the age wise deaths data. The data is class interval data. I have taken the mid values of the class interval.
I have applied the ...
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0answers
39 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?
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1answer
118 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, ...
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2answers
497 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 ...
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1answer
80 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
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1answer
179 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 ...
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1answer
155 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
398 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 ...
1
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1answer
4k views
Fitting truncated distributions using fitdistrplus with a lower bound of zero
I have been working to fit a normal distribution to data that is truncated to only be zero or greater. Given my data, which I have at the bottom, I previously used the following code:
...
4
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0answers
227 views
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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0answers
42 views
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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1answer
469 views
Left truncated survival data?
I am attempting Attrition Analysis in R using the Survival & KMsurv Package. My question is more related to how to use the R package / functionality for my situation.
Let us say the analysis is ...
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1answer
260 views
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1answer
461 views
Truncated distribution and mass points
If you have some continuous distribution $F(x)$ and you truncated the distribution at some inclusive point $m$ i.e. $F(x | x\ge m)$ does the truncated distribution have a mass point at $m$?
Also ...
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0answers
519 views
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:
...
2
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1answer
111 views
Unbiased estimators of a transformed Poisson
So the question I have is$:$
Let $X$ follow a Poisson distribution with mean $\mu$, except that $X=0$ cannot be observed; this gives a random variable $Y$ which has a truncated Poisson distribution ...
