# 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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### 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?
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 ...
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 ...
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 ...
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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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### 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 ...
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 ...
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### 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, let’s say, individual people, and associated & probability weights....
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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 ...
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. ...
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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 ...
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?
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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 , ...
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 > ...