Questions tagged [truncation]
Truncation is a process that results in the omission of data that are beyond a threshold.
138
questions
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1answer
49 views
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 ...
1
vote
1answer
37 views
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 ...
2
votes
1answer
61 views
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 ...
5
votes
1answer
162 views
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 ...
3
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0answers
96 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 ...
4
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0answers
62 views
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 ...
3
votes
1answer
61 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 ...
0
votes
1answer
27 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 ...
0
votes
1answer
15 views
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 ...
0
votes
0answers
10 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 ...
0
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0answers
10 views
Expectation of truncated autoregressive process
Consider the following nonlinear autoregressive model:
\begin{align*}
\epsilon_t & = \epsilon^\rho_{t-1} e^{u_t}, \\
x_t & = \frac{\gamma \, \epsilon_t x^a_{t-1}}{1+b y_t}, \\
y_t & = \...
0
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0answers
8 views
Valid to truncate KF state estimate?
In the field I study I have come across several cases where the Kalman Filter is used together with truncating the state estimate. The most recent case is a study where the algorithm cuts the ...
2
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0answers
18 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 ...
1
vote
1answer
159 views
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 ...
2
votes
1answer
25 views
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 ...
0
votes
1answer
42 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 ...
2
votes
2answers
216 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
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0answers
65 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
233 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
43 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
233 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
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0answers
43 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 ...
3
votes
1answer
72 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
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0answers
59 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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0answers
271 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
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0answers
69 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
29 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 ...
6
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1answer
2k 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
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0answers
86 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
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0answers
77 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
10.8k23 gold badges74 silver badges148 bronze badges
7
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1answer
3k 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
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
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2answers
493 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
35 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
460 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
248 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
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0answers
356 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
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0answers
56 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
442 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:
$$\text{Pr}(Y=1\,|\,X)=\Phi(...
5
votes
2answers
1k views
Mean vs. Trimmed mean in the normal distribution
In a simple experiment with the normal distribution in R I ran 500 iterations of a simulated normal distribution with N=100 each. For each iteration from the 500 iterations, I calculated both the ...
1
vote
1answer
95 views
Right, Left, Interval, Delayed, and truncted data
I have a medical data set that has all the following cases:
Right-censored
Left-censored
...
5
votes
1answer
393 views
Expectation of $X$ given $X < c$
Let $X$ be a random variable with PDF $f(\cdot)$ and CDF $\Phi(\cdot)$. I want to compute $E(X \mid X < c)$, where $c$ is some constant.
Using definition of the expected value
$$E(X \mid X < ...
2
votes
1answer
976 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
1k 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 a ...
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0answers
333 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 ...
2
votes
1answer
132 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 ...
1
vote
1answer
654 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
512 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
1k 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
81 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.
...
