Questions tagged [truncation]
Truncation is a process that results in the omission of data that are beyond a threshold.
36 questions
5
votes
1
answer
1k
views
The most general definition of the Likelihood function for continuous data (including truncation and censoring)
How would you rigorously define the likelihood function for censored/truncated observations? Even in most lifetime/reliability literature (where these types of observations are frequently encountered) ...
- 691
43
votes
1
answer
19k
views
Maximum likelihood estimators for a truncated distribution
Consider $N$ independent samples $S$ obtained from a random variable $X$ that is assumed to follow a truncated distribution (e.g. a truncated normal distribution) of known (finite) minimum and maximum ...
- 707
41
votes
2
answers
33k
views
What is the difference between censoring and truncation?
In the book Statistical Models and Methods for Lifetime Data , it is written :
Censoring: When an observation is incomplete due to some random cause.
Truncation: When the incomplete nature of ...
- 1,705
8
votes
2
answers
803
views
Truncated trivariate normal - conditional expectation
I am working on a paper in which I'd need to use the two following conditional expectations:
$E(X_{1}|a \leq X_{2} \leq b)$
$E(X_{1}|a \leq X_{2} \leq b, a \leq X_{3} \leq b)$
where $X_{1}, X_{2}, ...
- 91
23
votes
3
answers
22k
views
Simulate constrained normal on lower or upper bound in R
I'd like to generate random data from a constrained normal distribution using R.
For example I might want to simulate a variable from a normal distribution with ...
- 45.7k
16
votes
3
answers
10k
views
What does truncated distribution mean?
In a research article about sensitivity analysis of an ordinary differential equation model of a dynamic system, the author provided the distribution of a model parameter as Normal distribution (mean=...
anon
4
votes
1
answer
3k
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 ...
- 87
10
votes
1
answer
573
views
Properties of bivariate standard normal and implied conditional probability in the Roy model
Sorry for the long title, but my problem is quite specific and hard to explain in one title.
I am currently learning about the Roy Model (treatment effect analysis).
There is one derivation step at ...
- 270
4
votes
2
answers
382
views
Calculation of an "unconstrained" normal distribution (starting from a censored one)
Assume that two r.v. $W$ and $Y|W=w$ with
(1) $W \sim \text{N}(\mu_w,\sigma_w^2)$ (iid)
(2) $Y|W=w \sim \text{N}(w,\sigma_y^2)$ (iid)
Further we only observe $Y$ if $Y$ is less then $W$, i.e.,
(3)...
- 1,113
1
vote
1
answer
2k
views
Joint distribution of a Normal and Truncated Normal
I have a random variable $X\sim \text{Normal}(\mu,\sigma)$ and have the transformation $Y=\max\{0,X\}$. Is the distribution of $Y$ a truncated normal where it is truncated to live on the positive ...
user30490
15
votes
2
answers
4k
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 ...
- 329
14
votes
1
answer
10k
views
How to derive the mean and variance of a $k$-truncated Poisson?
How can I derive the mean and variance of a $k$-truncated Poisson? Here, $k$ is the cutoff value such that only values strictly larger than $k$ are allowed, i.e. the probability mass function is
$$...
- 141
11
votes
2
answers
10k
views
How should I model a continuous dependent variable in the $[0, \infty]$ range?
I have a dependent variable that can range from 0 to infinity, with 0s actually being correct observations. I understand censoring and Tobit models only apply when the actual value of $Y$ is partially ...
- 4,588
10
votes
2
answers
90k
views
How to calculate the truncated or trimmed mean?
How can I calculate the truncated or trimmed mean? Let's say truncated by 10%?
I can imagine how to do it if you have 10 entries or so, but how can I do it for a lot of entries?
- 471
9
votes
2
answers
11k
views
Survival analysis in R with left-truncated data
I am doing a survival analysis in R with the survival package.
I think I am working with left-truncated data, but I'm not entirely sure how to handle it.
I have a ...
- 131
6
votes
1
answer
274
views
Flawed multiple linear regression in academia? Heteroscedasticity's effect on p-value?
I believe I have found a paper in academia that has used a flawed multiple linear regression. I have downloaded the data set and replicated their regression results. I have done some diagnostics and ...
- 351
5
votes
0
answers
442
views
The marginals of a truncated multinomial are truncated binomials?
The multinomial distribution for a vector $\vec x$ of non-negative integers assigns a probability of:
$$f(\vec x) = n!\prod_i p_i^{x_i}/x_i!$$
to every vector $\vec x$ of non-negative integers in ...
- 4,552
5
votes
2
answers
3k
views
Expectation of $X$ given $X < c$
Let $X$ be a random variable with PDF $f(\cdot)$ and CDF $\Phi(\cdot)$. I want to compute $E(X \mid X < c)$, where $c$ is some constant.
Using definition of the expected value
$$E(X \mid X < ...
- 1,179
3
votes
0
answers
612
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 ...
- 1,478
2
votes
1
answer
688
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 ...
- 123
13
votes
2
answers
4k
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 ...
- 321
8
votes
3
answers
4k
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 $\...
- 787
6
votes
1
answer
9k
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:
...
- 205
6
votes
2
answers
825
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 ...
- 141k
4
votes
0
answers
97
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 ...
- 5,565
4
votes
1
answer
2k
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 ...
- 101
4
votes
1
answer
6k
views
How do I use the “survival” package and "Surv" function in R with left-truncated data?
I am trying to run survival analysis using the Surv and survfit functions from the survival ...
- 43
4
votes
3
answers
4k
views
Intepretation of Kaplan Meier with truncated and right censored data
I cannot seem to understand the interpretation of the Kaplan-Meier with truncated data.
Here, we have associated, with the j:th individual, a random age $L_j$
at which he/she enters the study and ...
- 691
4
votes
1
answer
2k
views
Exact distribution of sample mean of a continuous distribution
Please first note that I do know about the central limit theorem but I wish to derive an exact expression for the sample mean for any continuous distribution with probability density function $f(x)$. ...
- 41
3
votes
1
answer
815
views
Obtaining the Log-logistic distribution from a truncated logistic distribution
Let $$f(x) = \frac{e^x}{(1+e^x)^2}~,~ -\infty \lt x \lt \infty~~~~~(1)$$ be the standard logistic pdf of a random variable $X$. Then one can obtain the pdf of the log-logistic distribution via the ...
- 149
3
votes
1
answer
2k
views
Folded Normal and truncated Normal
Suppose to have a vector of random variables $\mathbf{y}$, distributed as a multivariate normal with mean vector $\boldsymbol{\mu}$ and covariance matrix $\boldsymbol{\Sigma}$.
The variable $\mathbf{...
- 1,322
2
votes
2
answers
1k
views
Appropriate distribution for bounded data set
I am designing a points-scored test. There is a limit on the maximum amount of points possible, as well as on the fewest amount of points possible. I have had a test group take the test and graphed ...
- 23
2
votes
1
answer
854
views
Creating a probability distribution that is truncated skewed
I have a dataset I want to use to generate a probability distribution. The distribution is skewed and can only include positive integers. I've tried normal (both skewed and truncated, although I can'...
- 33
2
votes
1
answer
1k
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 ...
- 121
2
votes
1
answer
861
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]
&...
- 135
1
vote
0
answers
438
views
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 ...
- 1,900