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.
50
questions
0
votes
0
answers
25
views
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 ...
- 13
1
vote
0
answers
35
views
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 $k$:
$...
- 145
1
vote
1
answer
112
views
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 ...
- 179
1
vote
1
answer
154
views
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 $...
- 153
2
votes
0
answers
38
views
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 ...
- 3,501
0
votes
1
answer
51
views
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 ...
- 165
3
votes
2
answers
113
views
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 ...
- 5,892
0
votes
1
answer
163
views
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}\...
- 115
1
vote
0
answers
48
views
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 } ...
- 523
1
vote
2
answers
120
views
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) ...
- 115
1
vote
0
answers
33
views
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 ...
- 157
5
votes
1
answer
497
views
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, \...
- 1,613
2
votes
1
answer
41
views
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 ...
- 614
0
votes
0
answers
48
views
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 ...
- 297
0
votes
0
answers
67
views
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 ...
1
vote
0
answers
237
views
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 ...
- 11
2
votes
0
answers
55
views
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 $E_{A}[x | x \leq t] \geq E_{B}[x | x \leq t]$, ...
- 21
3
votes
0
answers
34
views
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 ...
- 31
8
votes
2
answers
2k
views
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}{\...
3
votes
1
answer
73
views
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 $X$?
- 83
1
vote
1
answer
153
views
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, ...
- 302
0
votes
1
answer
336
views
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 ...
- 153
2
votes
0
answers
41
views
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 ...
- 21
1
vote
0
answers
196
views
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 ...
- 11
2
votes
2
answers
713
views
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?
- 53
3
votes
1
answer
358
views
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?
- 53
2
votes
1
answer
32
views
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 ...
- 23
3
votes
2
answers
1k
views
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 ...
user286826
1
vote
1
answer
34
views
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 ...
- 405
4
votes
1
answer
468
views
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 ...
- 53
0
votes
0
answers
194
views
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:
...
0
votes
0
answers
41
views
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 ...
- 1
1
vote
1
answer
146
views
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 ...
1
vote
1
answer
100
views
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 ...
0
votes
1
answer
52
views
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 ...
1
vote
0
answers
87
views
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 ...
- 11
0
votes
0
answers
13
views
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 ...
- 1
1
vote
2
answers
645
views
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 ...
- 21
1
vote
0
answers
763
views
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 ...
- 111
0
votes
1
answer
104
views
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 ...
- 5
8
votes
1
answer
771
views
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. ...
- 1,045
0
votes
0
answers
110
views
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 ...
- 63
0
votes
0
answers
15
views
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 ...
5
votes
1
answer
336
views
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?
- 71
2
votes
1
answer
83
views
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?
- 41
1
vote
1
answer
564
views
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 , ...
2
votes
1
answer
1k
views
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 > ...
- 23
1
vote
1
answer
38
views
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....
- 121
3
votes
1
answer
75
views
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 ...
15
votes
3
answers
4k
views
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 ...
Catrin Campbell-Moore