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24 views

Conditional moments of bivariate normal

Suppose that (X,Y) are bivariate normal with non-zero means and correlation. Is there any neat expression for $\mathbb{E}(X|Y>0)$?
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0answers
37 views

Proving a “well-known” result regarding the distribution of a normally distributed random variable

In an important project work, I would like to include a "proof" of the following, but have unfortunately been unable to readily compute it myself. I am aware that this is a flaw on my part, but ...
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0answers
41 views

Regression with dependent variable which ranges from -1 to 1

I performed a series of Pearson correlations which give me as expected values between -1 and 1 (actually very few below zero). I'd like now to see if some factors are linked to these correlation ...
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0answers
23 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) ...
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0answers
16 views

Conditional expectation in mixture distributions

I have a mixture distribution for observed lifetime data $(\delta_i,t_i,L_i)$, where $\delta_i$ is a censoring variable (1 indicating death, and 0 indicating censoring), $t_i$ is the observed lifetime ...
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0answers
18 views

Continuous low truncated response in regression

I can't find a clear answer on how to model a regression with a low bounded response. The tipical case is with response variables that can take only positive results. Poisson and negative binomial ...
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2answers
1k 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 ...
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2answers
164 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 ...
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0answers
205 views

Two-part models in R: continuous outcome with too many zeros

I am estimating a model where the outcome variable is continuous, more specifically a percentage in the form of a 0 to 1 range. This variable has one potential problem: many of its cases equal zero ...
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1answer
29 views

Correlation with one variable missing half of its values

Let´s say I want to run a correlation between "eye spherical defect" and height and I want to use only individuals with myopia, whose "spherical defect" goes from 0 to -20 or so. Whereas the ...
3
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3answers
206 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 ...
3
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0answers
155 views

Is there a way to model left truncated and interval censored data in R or SAS?

We have a study where our participant underwent some surgery at time = 0, but at various ages. Our follow-up is based only on Medicare age-eligible people, so we have to wait until they reach the age ...
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0answers
40 views

proper one-sided test for truncated distribution

I have positional segments that contain N number of mutations. Each mutation has a frequency which is determined by taking the number of reads supporting the alternate allele (r) and dividing them by ...
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0answers
35 views

Estimating parameters in a truncated binomial distr

I would like to find the estimates of the parameters in a truncated (at zero) negative binomial distribution.Suppose $Z$ has this distribution with parameters ($\alpha,\beta$). (The parametrization ...
1
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1answer
87 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 ...
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1answer
59 views

Sum of truncated normal distributions with other distributions (like uniform) that have partially common domains

I have some truncated normal distributions and some other distributions (like uniform distribution) that have partially common domains. I'd like to know how can I calculate the entropy for the sum of ...
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0answers
39 views

Clarify terminology regarding truncated and censored distributions [duplicate]

I'm looking for clarification on the definition of truncated distributions and on terminology for censored distributions and truncated distributions. I recently had a [dialog on SO][1] regarding [a ...
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2answers
90 views

Calculating $\overline{X}$ and $S(X)$ for a truncated Normal distribution

I have the following dataset which appears to be normally distributed but is truncated at 0. If I ignore the values which are 0 I get an even better distribituion. I would like to conclude that ...
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0answers
101 views

Censored data from a truncated distribution (Stan)

I'm trying to write a survival model of fossil species durations. In this case, the minimal possible duration for a species is 1. Also, the general idea in paleontology is that we are only observing a ...
2
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1answer
115 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 ...
0
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1answer
31 views

Running regressions on subsamples: Include the variable on which the subsample is based in the regressions?

Income is one of my independent variables in a sample of 2000 households. I'd like split the sample along household income lines (poor, vulnerable and non-poor). Is there a reason not to include ...
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0answers
49 views

Run Tobit with missing values (from linear prediction) or change them to zeros - STATA “practical” question

I want to run a Tobit linear regression in order to especify a labor-supply curve (linear-linear). As dependent variables I have personal characteristics, enviromental ones, and wages (predicted using ...
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0answers
117 views

Truncated Gamma distribution parameter estimation

I need to estimate the parameter of a Gamma distribution form the data, but I only have samples from 0.05 to 3 (most of the samples are concentrated here). I tried MLE but due to the truncation is ...
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0answers
16 views

error on truncated rms

I am computing the RMS of a sample to estimate the standar error $\sigma$ of the underlying distribution (for simplicity let say a normal distribution $N[\mu$, $\sigma$]). $ \text{RMS} = \sum_{i=1}^N ...
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1answer
36 views

Area under a truncated distribution = 1

I have computed a truncated normal distribution, which total probability density (i.e. area under the curve) is equal to 0.92. The distribution represents well the reality of the phenomenon I am ...
3
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2answers
490 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 ...
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1answer
203 views

Sum of normal truncated random variables

Suppose I have $n$ independent normal random variables $$X_1 \sim \mathrm{N}(\mu_1, \sigma_1^2)\\X_2 \sim \mathrm{N}(\mu_2, \sigma_2^2)\\\vdots\\X_n \sim \mathrm{N}(\mu_n, \sigma_n^2)$$ and ...
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0answers
58 views

Truncated normal in WinBUGS

I want to use the following truncated normal distribution in WinBUGS to estimate parameters of SEM using Bayesian analysis. ...
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1answer
59 views

How can I estimate the tail of a distribution with a truncated distribution?

The broadband speed data I'm working with have all values over 30Mbps placed into a >30 category. The distribution is thus truncated. This leads to the final column in the histogram below being a ...
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1answer
154 views

Expectation of Truncated & Random Variable

I have what appears to be a relatively simple question, but am struggling to understand how to go about answering it. The general question is as follows: What is the expected value of $S_{I}$, ...
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0answers
75 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 ...
2
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2answers
107 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 ...
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3answers
4k views

What are the relative merits of Winsorizing vs. Trimming data?

Winsorizing data means to replace the extreme values of a data set with a certain percentile value from each end, while Trimming or Truncating involves removing those extreme values. I always see ...
2
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1answer
126 views

Way to correct sample selection bias with unknown selection?

I would greatly appreciate some advise on a statistical problem that haunts me. Suppose you wish to estimate the effect of $x$ on $y$, but the probability to observe $\{y_i, x_i\}$ also depends on ...
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0answers
76 views

Error of data fitting by gamma.fit() in Python

I need to find gamma fit for data in Python 3.2. param = gamma.fit(samp) // samp is a list of floating point numbers I got error: ...
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0answers
84 views

General truncated Poisson distribution: R routines

I face an applicaton with (a possible) five-truncated Poisson distribution - I count periods at least five days long, thus data of the type (5, 8, 12, 5, 5, 10, ...). Much theory and software is ...
2
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1answer
120 views

Can we still use OLS on truncated a $Y$ if its conditional distribution is normal?

I was recently reading about Heckman selection models, and got sidetracked by how little I knew about truncated data. I was reading these slides, and on page 78 Baum mentions that if part of a sample ...
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1answer
164 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 ...
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2answers
104 views

Response variable bounded by dependent variable

I have a problem: y~x1+x2+x3+x4 where the response variable y is always more than or equal to the explanatory variable x1 (for e.g. x1 represents the income of one person in a couple and y is the ...
3
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0answers
101 views

Truncated Explanatory Variable

I am running a model where one of the explanatory variables is truncated. In particular, the variable measures the duration of unemployment (retrospectively) in months and it is truncated at 2 years, ...
2
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1answer
61 views

$E(x^k)$ under truncated $\mathcal{N}(\mu,1)$

There is a similar question in $E(x^k)$ under a Gaussian. However, it doesn't seem to be trivial when $\mu\ne0$. As mentioned in the previous question $k$ is not an integer. The integral that I need ...
2
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1answer
65 views

Joint probability of two correlated RVs

I am trying to get the joint PDF of two RVs $X$ and $Y$ where $aX<Y<bX$, so I am stuck in calculating the probability of $\mathbb{P}(X<x,Y<y|aX<Y<bX)$ any idea?
2
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1answer
837 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 ...
3
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2answers
217 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., ...
2
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1answer
350 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 $f(x)$. ...
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1answer
185 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 ...
2
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2answers
297 views

Pre-truncation moments for truncated multivariate normal

Suppose the random variable $Y$ has a multivariate normal (MVN) distribution, and consider truncating $Y$ in some way to create $T$. Given $T$'s mean and covariance matrix, I'd like to obtain $Y$'s ...
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1answer
344 views

Truncated Normal — Reproduce a randomly generated data set

help. Problem: Given a bounded Gaussian Distribution -- looking reproduce similar results i.e. same mean and standard deviation randomly. Definition: Data set exhibits properties of a Gaussian ...
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2answers
1k 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 ...
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0answers
538 views

Finite mixture models with bounded data

I am trying to fit a finite mixture model to a dependent variable which is bounded (practically) between -0.594 and 1 (theoretically, the latent variable is bounded between -Inf - 1). The data are ...