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12 views

How do I fit a set of data that has a lower and upper bound to a lognormal distribution in R?

I have data only above 200,000 and up to 1,000,000, is there a simple R command that will permit me to fit a lognormal distribution to this data? Same for a pareto distribution?
2
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1answer
28 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 ...
1
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0answers
23 views

Truncated distribution $f(x;\theta)=\theta x^{-(\theta-1)}$

I'm trying to derive for p.m.f. $$f(x;\theta)=\theta x^{-(\theta-1)}$$ $x>1, \theta > 0$ the truncated distribution that excludes observations $1<X≤a$ $$f(x | X > ...
3
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0answers
54 views

Why is this Bayesian estimate of a truncation-point so poor?

I have several datasets. Each dataset holds the masses of objects that have been subject to physical wear, expressed as a proportion of their original mass ($w$), and the amount of time that the ...
0
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0answers
16 views

Draw samples from distribution that add up to specific value

I'm currently working on a fire distribution model in which fire sizes are log-normally distributed. In my simulation, in each time step, fire sizes are sampled and summed up until a certain fixed ...
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0answers
26 views

Regression method if dependent variable is the absolute value of a continous variable [duplicate]

Suppose we have a dependent variable $Y$ that has normal distribution with a mean of $0$. If I run a regression model using the absolute value of $Y$, $|Y|$, i.e. $|Y| = b_1 + b_2 X + u$, my dependent ...
2
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0answers
36 views

Unbiased Estimator of the truncation points in a truncated normal distribution?

Consider the variables $x_i \text{~} \mathcal{N}(\mu, \sigma^2,a,b)$ iid with truncation points $a$ and $b$, i.e. $a < x_i < b$. Suppose all 4 parameters, namely $\mu, \sigma, a, b$ are all ...
4
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1answer
77 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 ...
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0answers
59 views

Mean of a truncated quadratic function of a normal variable

Suppose you want to compute the mean of the following random variable: $$ V=\left(\frac{z-y}{z}\right)I\left(y<z\right)-\left(\frac{z-b_0}{z}\right)I\left(b_0<z\right) $$ where: $$ ...
2
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0answers
65 views

Truncated power basis function and continuity in b-splines

I do not understand how adding a truncated power basis function leads to continuity in B-Splines. Could someone please provide a low level explanation?
1
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2answers
56 views

Appropriate priors for truncated regression model

I have a simple linear regression model with the constraint that my dependent variable y (response time) has to be greater than zero. I want to specify priors for intercept, slope and sigma (the ...
2
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1answer
140 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 ...
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0answers
44 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}, ...
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0answers
29 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 $\mathbb{E}(X|Y>0)$?
2
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0answers
60 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
48 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
43 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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2answers
6k 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
759 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
696 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
38 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 ...
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3answers
581 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 ...
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0answers
332 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 ...
2
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0answers
46 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 ...
3
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0answers
139 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
124 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
100 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 ...
2
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0answers
42 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 ...
0
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2answers
105 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 ...
0
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1answer
314 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 ...
3
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1answer
210 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
48 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 ...
3
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0answers
285 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
23 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 ...
1
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1answer
60 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 ...
4
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2answers
1k 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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2answers
299 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
67 views

Truncated normal in WinBUGS

I want to use the following truncated normal distribution in WinBUGS to estimate parameters of SEM using Bayesian analysis. ...
4
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1answer
105 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 ...
1
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1answer
440 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 $S_{I}$, ...
1
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0answers
135 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
161 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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4answers
9k 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
153 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
112 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
144 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
149 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
247 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 ...
1
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2answers
128 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
158 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, ...