Questions tagged [truncated-distributions]

A truncated distribution is one that is cut off at some value, either at the low or high end of the distribution, or both.

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Understanding truncated distributions & simulations [duplicate]

I have a data set which follows lognormal distribution (parameters $μ$, $σ$ known - estimated by maximum likelihood estimation). I have to generate random numbers within range $[a:b]$ from this known ...
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Is it possible to prove that this function of the truncated binomial is decreasing?

Suppose a random variable is binomially distributed with $G$ trials and success probability $p$. Consider the expected proportion of successes, given that the proportion of successes is at least $k$: $...
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Fitting truncated normal mixtures in R

I have a vector x, lower_bound < x < upper_bound. I would like to fit a truncated normal mixture distribution to ...
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Knowing the sum, the n(), and the bound parameters of a truncated-Pareto distributed variable, how I identify the alpha (shape) parameter?

I know that there would be a fancy command on R to do the estimation of $\alpha$ given the inputs, but I am also curious about the relationship between $\alpha$ to $...
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Conditional expectation of $X_t$ in a time series, given that other draws were below $c$

I'm interested in the moments of a given draw, $X_t$, of a time series conditional on the knowledge that all other draws within some window before and after $t$ were below a fixed threshold, $c$. For ...
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Difference of means with a truncated distribution

Let's say I'm measuring viral load post-infection. The two groups I have are vaccinated and unvaccinated. We expect the distribution of the unvaccinated cohort's viral load to resemble a normal ...
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Why are Truncated Probability Distributions important in Statistics?

Why are Truncated Probability Distributions important in statistics? Recently, I was reading about "Truncated" Probability Distributions. As the name suggests, a Truncated Probability ...
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Why I cannot generate random numbers having a truncated lognormal distribution?

My deduction is: When the distribution is truncated, a normalization factor should be introduced: \begin{equation} g(x) = \frac{C}{x\sigma\sqrt{2\pi}}e^{-\frac{1}{2}\left(\frac{\ln{x}-\mu}{\sigma}\...
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How to compute the PDF of a conditional distribution [duplicate]

Let $T \sim Unif(0, 1)$. Then, $f_T(t) = 1 \text{ for } t \text{ in [0, 1] (0 elsewhere)}$. How do we formally compute $f_{T \mid T > 0.5}$? Intuitively, $f_{T \mid T > 0.5}(t) = 2 \text{ for } ...
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True mean of a truncated distribution?

I use C++ GSL library to generate random numbers now. The numbers obey a distribution, (e.g. normal or lognormal distribution). This library requires the input of expected value ${\mu}$ (i.e. mean) ...
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Output Distribution of ReLU given a Laplace Distribution as its Input

If input to a ReLU function (Max(X, 0)) is a Laplace Distribution, what would be the output distribution? will it have a density function? how would it look like? assuming that mean of the Laplace is ...
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Understanding the pdf of a truncated normal distribution

Suppose $\boldsymbol{x} = (x_1, \ldots, x_m)^T$ follows a multivariate normal distribution with 2-sided truncation $a_i \leq x_i \leq b_i$. This is a truncated multivariate normal defined by $TN(\mu, \...
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Data count regression with a truncated distribution

Imagine that we are conducting an experiment to test the effectiveness of a treatment, where the «level of illness» is measured by a count that is distributed as a negative binomial (NB). The plan is ...
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Enforcing conditions on truncated exponential distribution

The CDF for an exponential distribution of rate $\lambda$ truncated at T is $F(t) = \frac{1-e^{-\lambda t}}{1-e^{-\lambda T}}$. (for $t<T$, else 0). I would like to determine $\lambda$ and $T$ such ...
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how to compute marginal effects of predictors in NBSTRAT (truncated & endogenously stratified negative binomial) model? (Stata)

I'm using STATA 16.0 to develop recreational demand function via using NBSTRAT model. I have several factor and continuous variables that force me to use "xi:" prefix in the model syntax ...
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Finding Confidence Interval for Lower Bounded Truncated Normal Distribution

I am working on finding a confidence interval for data that follows a lower bounded truncated normal distribution (lbtnd) bounded from 0 to $\infty$. I am having difficulty completely understanding ...
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Mean preserving spread and truncated distributions

Take two distributions $F_B(x)$, $F_A(x)$ with the same support. Assume that B is a mean-preserving spread of A. What I want to understand is whether $E_{A}[x | x \leq t] \geq E_{B}[x | x \leq t]$, ...
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Truncated expectation of sum of independent random variables

Take three random variables $X$, $Y$, $Z$ s.t. $E[X]>0$, $E[Y|X]=0$, $Z = X+Y$. What can I say about $E[x| x> k]$ vs. $E[z| z>k]$ where $k>0$? Intuitively, the latter should be bigger ...
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Generating random samples obeying the exponential distribution with a given min and max

Random samples obeying the exponential distribution can be generated by the inverse sampling technique by using the quantile function of the exponential distribution: $$ x = F^{-1}(u) = - \frac{1}{\...
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Dominance of truncated means

If for two random variables, the truncated mean of one is always larger than the other, i.e. $E(Y|Y<x)>E(X|X<x)$ for all $x$, can we infer that $Y$ first-order stochastically dominate $X$?
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Completeness of a statistic in a truncated distribution

Suppose a random sample $x_1,\dots, x_n$ (i.i.d.) from a random variable $X$ defined over $(\Omega,\mathcal{F},P)$ whose probability density function is $f(x_1,\dots, x_n;\theta)$ and $T(x_1,\dots, ...
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Truncated normal distribution without scaling

My understanding of a truncated normal distribution $\mathcal{N}(\mu,\sigma;a,b)$ is that it results from scaling the values of a normal distribution within the bounds $[a; b]$ such that the area ...
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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 ...
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Confidence interval for the maximum likelihood estimate of the minimum of a left truncated exponential distribution

I am currently working on a problem in which I have observations $y_{i}$ that are distributed, $y_{i} \sim \textrm{Exponential}(\beta = ax_{i})\cdot T[b, \infty)$ where, $\beta$ is the rate parameter ...
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Conditional expectation of a Gamma Distribution

$X$ a Gamma Distributed random variable. Calculate $E[X\mid X \in [a,b]]$, where $a>0$, $b>0$. Is there a closed form solution for this, and if so, how can I calculate it?
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Conditional expectation of a Weibull distributed random variable

Let $X$ be a Weibull Distributed random variable. I want to calculate $E[X\mid X \in [a,b]]$, where $a>0$, $b>0$. Is there a closed form solution for this, and if so, how can I calculate it?
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What is the correct probability distirbution for the given situation?

A game is played until either a player receives their 3rd loss or their 7th win. What is the distribution of the number of wins that the player gets before their 3rd loss? I was thinking of using a ...
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How would you find the mean of the zero truncated Poisson distribution? [closed]

Given the probability mass function is, $f_T(y)=P(Y=y|Y>0)= \frac{1}{e^\lambda -1} \cdot \frac{\lambda^y}{y!}, y=1,2,3,\dots$ Where, $f(y)=\frac{e^{-\lambda}\lambda^y}{y!},y=0,1,..$ How would ...
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Truncated CEF of normally distributed RV. Is sample analogue a consistent estimator of the 'population' truncated CEF?

If I have a random variable that is normally distributed, and truncated such that I only see $y$ if $y\geq 0$, and I want to do some calculations with the truncated Conditional Expectation Function in ...
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What is the characteristic function of a rectified Normal distribution?

Rectified Normal distribution is a hybrid distribution with the following pdf: $f(x;\mu ,\sigma ^{2})=\Phi (-{\frac {\mu }{\sigma }})\delta (x)+{\frac {1}{{\sqrt {2\pi \sigma ^{2}}}}}\;e^{{-{\frac ...
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Two intercepts for zero-truncated negative binomial model using VGAM

I am trying to understand the first and second intercept for the zero-truncated negative binomial regression model I estimated using VGAM. Below is my syntax: ...
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confidence interval for mean based on small sample when CLT does not hold

I have looked at similar questions but could not find an satisfactory answer. Please forgive if I'm wrong. I have a small sample (n = 24) and use the sample mean as estimator of the true mean. I want ...
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Implementing a truncated regression for a normal distribution in R

I'm not a statistician but I'm working with some experimental psychology data. I have a distribution of responses on a -4 to 4 scale. Usually, these type of variables is treated as continuous. I have ...
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Regression with ranked and truncated dependent variable

I'm struggling to find a model that will best fit this data. The dependent variable is the ranking of a observation based on how many votes it received based of a list of choices (number of votes is ...
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Bounds on dependent truncated random variable with given mean and variance

I have two random variables $X$ and $Y$ with given (mean, standard deviation) as $(\mu_{X}, \sigma_{X})$ and $(\mu_{Y}, \sigma_{Y})$, respectively. These random variables have their truncated ...
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Precision issues using truncnorm in R [closed]

I'm facing some precision issues with truncnorm, particularly the ptruncnorm() function in R. Here's an example where I find the cdf up to $q= 2$, where the truncation point is $1.9$, for several ...
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Estimating false accept rates from imposter scores below a threshold

I have a system that compares two items and produces a match score. Scores below a threshold are manually inspected to determine if they match or don't(imposter). Scores above the threshold are ...
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two sample analysis with outliers

I've got some data from two groups which have different sample size. (univariate variable like 'price', and want to test whether they have significant difference ) The sample size of 'A' is 10,000 ...
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How to get a random function with a truncated normal distribution? [duplicate]

My goal is to have a function that given an input value will output a random value that follow a truncated normal distribution, could you please suggest a function that can do that ? Or guide me a ...
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Dealing with measurements falling outside of the theoretical range/boundaries of the data

Imagine I am measuring a bounded variable (with a maximum possible value above which the data doesn't make sense) and I end up with the following dataset with my measurements and measurement errors as ...
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Calculating the expected value of truncated normal

Using the mills ratio result, let $X \sim N(\mu, \sigma^2)$, then $E(X| X<\alpha) = \mu - \sigma\frac{\phi(\frac{a- \mu}{\sigma})}{\Phi(\frac{a-\mu}{\sigma})}$ However, when calculating it in R. ...
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How to properly truncate exponential distribution to represent random memory-less arrivals?

Typically, Poisson and exponential distributions are used to represent random memory-less arrival processes. It has come to my attention, however, that a more realistic distribution is a truncated (or ...
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Distribution of (bounded) quiz scores

Our office does the daily quiz. Mostly we get around 8/10. We can not go outside the range 0-10, and at both those limits there is a non-zero probability. What parametric distribution might be ...
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Truncated Gamma Distribution

The Gamma distribution is the conjugate prior of Poisson distribution. What about the Truncated Gamma distribution? Is it still the conjugate prior of Poisson distribution?
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Mean of truncated distribution

Is the mean of a left truncated distribution always greater than equal to the original mean? Or is that only for certain distributions?
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Mean of a truncated non-standard beta distribution

I have a non-standard beta distribution in the interval [-0.02 , 0.005] (as opposed to [0,1]). I know its mean and variance (and thus α and β). I want to calculate the mean of its truncation to [0 , ...
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2 votes
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Mean of truncated gamma distribution using threshold

Given a gamma distribution with PDF: $f(x;\alpha;\beta) = \frac{x^{\alpha-1} e^{-\frac{x}{\beta}}}{\Gamma(\alpha) \beta^\alpha}$ with a shape parameter $\alpha > 0$, a scale parameter $\beta > ...
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1 vote
1 answer
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How to parameterise a known distribution with mean, standard deviation and fixed upper and lower bounds?

I am looking for something resembling the normal distribution but which is capped at 0 and some size N. The average can be at any point between 0 and N, and there exists a specified standard deviation....
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Linear regression: how to treat an explanatory variable that is discrete but does not have a natural zero

Background/study system: One of my MS students is studying the biomechanics of strand breakage in Spanish moss (an epiphyte--or plant that lives on other plants). Spanish moss has strands that can ...
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15 votes
3 answers
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Estimating mean and st dev of a truncated gaussian curve without spike

Suppose I have a black box that generates data following a normal distribution with mean m and standard deviation s. Suppose, however, that whenever it outputs a value < 0 it does not record ...
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