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0answers
15 views

Likelihood function with truncated normal distribution [on hold]

I have a system of 3 equations with a normal distribution. \begin{align} P_{dt} &= α_0 + α_1X_{1t} + α_2X_{2t} + ε_{1t} \\ P_{st} &= β_0 + β_1X_{3t} + β_2X_{4t} + ε_{2t} \\ P_t &= ...
1
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0answers
10 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
17 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
84 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 ...
6
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1answer
111 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 ...
2
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0answers
38 views

Truncated normal in WinBUGS

I want to use the following truncated normal distribution in WinBUGS to estimate parameters of SEM using Bayesian analysis. ...
3
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1answer
37 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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0answers
31 views

Is this method for mixing doubly Truncated Normal distribution acceptable?

Say I have to mix n double Truncated Normal distributions $\textit{TNormal(μ,σ$^{2}$,0,1)}$. Furthermore, each distribution has a weight w. w represents the influence of the distribution in the ...
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1answer
40 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
29 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
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2answers
57 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 ...
11
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3answers
692 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
100 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 ...
1
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0answers
48 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: ...
1
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0answers
34 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
90 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 ...
0
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1answer
85 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
76 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 ...
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0answers
44 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
56 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
53 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
283 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
204 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
248 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 $f(x)$. ...
8
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1answer
165 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 ...
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2answers
207 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 ...
1
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1answer
247 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
452 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 ...
2
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0answers
309 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 ...
0
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1answer
629 views

WinBUGS truncated normal distribution [duplicate]

I am estimating a stochastic frontier with a mixed model. So far the half normal distribution worked good but I need a truncated normal distribution. It does not work, and I receive the error ...
11
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1answer
2k 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 ...
6
votes
1answer
606 views

What is the Fisher information for the truncated poisson distribution?

The zero-truncated poisson distribution has probability mass function: $$P(X=k) = \frac{e^{-\lambda}\lambda^k}{(1-e^{-\lambda})k!}$$, $k=1,2,...$ And the expectation of the truncated Poisson ...
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2answers
843 views

Are truncated numbers from a random number generator still 'random'?

Here 'truncating' implies reducing precision of the random numbers and not truncating the series of random numbers. For example, if I have $n$ truly random numbers (drawn from any distribution, e.g., ...
2
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0answers
61 views

Where can I get reference formulas for truncated distributions?

I have been comparing tails of various distributions for an application where we will need the conditional expectation of the tail or a truncated tail: $E(X | a<X \leq b )= \frac{\int_a^b x f(x) ...
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2answers
242 views

Combining the results of two surveys

Someone has surveyed a number of people and put the results in a database (Survey 1). Each observation has additional information that, for any subpopulation (men only, young only, etc.), gives a ...
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3answers
1k 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 ...
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2answers
520 views

Is sampling from a folded normal distribution equivalent to sampling from a normal distribution truncated at 0?

I wish to simulate from a normal density (say mean=1, sd=1) but only want positive values. One way is to simulate from a normal and take the absolute value. I think of this as a folded normal. I ...
12
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4answers
2k views

R/Stata package for zero-truncated negative binomial GEE?

this is my first post. I'm truly grateful for this community. I am trying to analyze longitudinal count data that is zero-truncated (probability that response variable = 0 is 0), and the mean != ...
5
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2answers
1k views

Censoring/Truncation in JAGS

I have a question on how to fit a censoring problem in JAGS. I observe a bivariate mixture normal where the X values have measurement error. I would like to model the true underlying 'means' of the ...
4
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2answers
16k 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?