A truncated distribution is one that is cut off at some value, either at the low or high end of the distribution, or both.
Questions tagged [truncated-distributions]
47 questions
15
votes
3 answers
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 anything (can't even tell that it's outputted such a…
Catrin Campbell-Moore
8
votes
2 answers
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:
$$
x = F^{-1}(u) = - \frac{1}{\lambda} \ln(u)
$$
where $u$ is a sample drawn from…
Herpes Free Engineer
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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. I don't obtain the correct results as
> mu <- 1
>…
Kozolovska
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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 $TN(\mu, \Sigma, a, b)$ where $a = (a_1, \ldots, a_m)^T$…
Adrian
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5
votes
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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?
Suki Hao
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4
votes
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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 {(x-\mu )^{2}}{2\sigma ^{2}}}}}{\textrm …
Ramin Barati
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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 but I have failed to (dis)prove it. Any hint/reference?
user312267
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3
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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|YE(X|X
AnonA
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3
votes
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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?
M N
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3
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How would you find the mean of the zero truncated Poisson distribution?
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 you show that mean of this function is,…
user286826
3
votes
1 answer
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 grow into larger clumps of strands…
coreydevinanderson
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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 example, I might want the expectation of $X_{80}$…
half-pass
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2
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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 to use a mixed GLM for NB distributed…
Arnaud Mortier
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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 $E_{A}[x | x \leq t] \geq E_{B}[x | x \leq t]$, but I'm struggling. From the definition of…
user313975
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2
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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 very large datasets, composed of millions of…
Dave Bapst
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