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# 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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### Truncated distribution and hazard rates in a microeconomic model

I'm trying to prove something related to a labor microeconomic model: t∈{1,2,3}, A∼N(0,1) (A is fixed across periods), εt∼N(0,1) (εt are independent for every εt), c>0 is the cutoff for promotion ...
1 vote
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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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1 vote
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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 ...
358 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: g(x) = \frac{C}{x\sigma\sqrt{2\pi}}e^{-\frac{1}{2}\left(\frac{\ln{x}-\mu}{\sigma}\...
1 vote
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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 ...
143 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 ...
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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 ...
1 vote
639 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 ...
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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}{\...
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 $X$?