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.
30
questions
1
vote
0answers
54 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 ...
2
votes
2answers
39 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?
2
votes
1answer
34 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?
0
votes
0answers
13 views
Inferring truncated distribution and mortality rates from age-binned population data
Ultimate goal: compare age-specific and age-standardized mortality rates between two populations with different age distributions.
The population data are in age bins (slightly different for each ...
2
votes
1answer
28 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 ...
3
votes
2answers
168 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 ...
1
vote
1answer
21 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 ...
1
vote
1answer
50 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 ...
0
votes
0answers
19 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:
mod.negb <- vglm(ED_Visit ~ Male + ...
0
votes
0answers
27 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 ...
0
votes
0answers
33 views
Angle of Line in a non-Normal Q-Q Plot
I'm currently working on a toy-problem of $n=15$ data-points and believe that my data may have come from a Truncated Normal Distribution with a lower-bound of $a=5.0$.
I'm using the R's ...
0
votes
0answers
21 views
Calculating the truncated version of the squared hyperbolic secant PDF
$
\newcommand{\sech}{\mathop{\rm sech}\nolimits}
$
Hello,
I have the following Probability Density Function (PDF):
$f(x)=\frac{1}{2s}(\sech\frac{x}{s})^2$
This PDF has support for $x\in(-\...
1
vote
1answer
32 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
1answer
21 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
1answer
27 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
0answers
32 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 ...
0
votes
0answers
16 views
Comparing empirical and theoretical estimates of the number of right-censored values
Suppose I have right-censored data, so that observations are still present but are top-coded. In my case this is income data for, letās say, individual people, and associated & probability weights....
0
votes
0answers
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
vote
2answers
74 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 ...
1
vote
0answers
324 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 ...
0
votes
1answer
41 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 ...
7
votes
1answer
500 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. ...
0
votes
0answers
43 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 ...
0
votes
0answers
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
1answer
188 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?
2
votes
1answer
50 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?
1
vote
1answer
259 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 Ī± and Ī²).
I want to calculate the mean of its truncation to [0 , ...
2
votes
1answer
386 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 > ...
1
vote
1answer
23 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....
3
votes
1answer
68 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 ...
