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.

Filter by
Sorted by
Tagged with
2 votes
0 answers
30 views

Distribution supported on $(0,\infty)$ for which moments of its truncated distribution are elementary functions of the truncation point and power

I am looking for a distribution with a differentiable PDF $f:(0,\infty)\rightarrow (0,\infty)$ for which for any $\delta>1,z>0$, the two following integrals are finite elementary functions of $\...
cfp's user avatar
  • 535
3 votes
0 answers
58 views

What is the PMF of the Zero-Truncated Skellam distribution?

Vaguely related to the notion of a Lindley equation, I am considering a recurrence $$L_{t+1} := L_t + \max \left( 0, A_t - S_t \right)$$ where $$L_t$$ is the number of customers in a queue system at ...
Galen's user avatar
  • 8,125
4 votes
1 answer
124 views

glmmTMB truncated models with zero inflation

everyone. I am fitting a glmm model using the R library glmmTMB for predicting a count response variable with excess-zeros and overdispersion (...
Javier's user avatar
  • 43
2 votes
1 answer
121 views

A question related to the convergence of mathematical expectations restricted to an Interval centered on zero

Let $(X_j)_{j= \mathbb 0}^\infty$ a fixed realization of strictly stationary AR(1) process: $$X_j = 0.9 \,X_{j-1}+ \eta_{j}, \quad (\eta_j) \overset{iid}{\sim} N(0,1)$$ For each $n$, consider $B_n\sim ...
André Goulart's user avatar
0 votes
0 answers
40 views

Limit on percentile of conditional expectation

I'm studying which percentile is the expected value of a continuous random variable $X$ given $X<t$ in the left limit of X, which is equivalent to computing the limit \begin{equation} L = \lim_{t \...
Bridi's user avatar
  • 1
1 vote
0 answers
39 views

Develop a model for theoretical best performances at different ultra running distances/times

Goal Develop a model for theoretical best performance for running distances from marathon to around 1000 km. Partly to compare the strength of ultrarunning world records, but more importantly, to get ...
Daniel Westergren's user avatar
1 vote
0 answers
34 views

Generalized likelihood ratio test for a left-truncated exponential distribution [duplicate]

I am doing self study in statistical inference and am rather confused about how to approach generalized likelihood ratio test (GLRT) problems. I am trying the traditional approach by definition and ...
392781's user avatar
  • 160
2 votes
0 answers
126 views

Mixed model with censored data in R?

My objective is to see if there is a significant difference in BHB concentration between age categories in farm animals. Farm should be a random effect in the model. The issue is that BHB ...
Falco's user avatar
  • 139
0 votes
1 answer
52 views

Truncated lognormal distribution calibration with MME

To estimate the parameters of a truncated distribution (lognormal for example), we can use the Maximum Likelihood Estimation or Method of Moments. For the Method of Moments Estimation, one needs to ...
John Smith's user avatar
0 votes
1 answer
133 views

Expected value of Truncated Normal Distribution [duplicate]

For the truncated normal distribution below: $$ {f_X(x; σ, a, b)} = \frac{1}{\sigma}\frac{φ(\frac{x-µ}{σ})}{Φ(\frac{b-µ}{σ})-Φ(\frac{a-µ}{σ})} $$ $$ a = 1; b = ∞; σ = 2 $$ I need to calculate the ...
nilsinelabore's user avatar
4 votes
1 answer
382 views

How to use Truncated Normal for observation distribution in GLM model?

I'm trying to setup a Bayesian GLM with Truncated Normal, $\mathcal{N}_+(\mu, \sigma, 0)$ truncated at $0$. I want to specify $\mathbf{E} (y\mid x) = ax + b$ but it looks like $\mathbf{E} (y\mid x)$ ...
chesslad's user avatar
  • 211
2 votes
1 answer
139 views

How to combine two truncated distributions

We want to combine two truncated distributions to better model one phenomenon. For example, we have a Gaussian distribution, but we want to modify the right hand side tail to make it heavier. So we ...
John Smith's user avatar
0 votes
0 answers
44 views

Central limit theorem : relaxing assumption of all finite moments

Consider $S_n = \sum_{i = 1}^n b_{i,n} X_{i,n}$ where $X_{i,n}$ are random variable neither independent neither identically distribution and $b_{i,n}$ are weights satisfying the Lindeberg condition. I ...
Eryna's user avatar
  • 309
2 votes
1 answer
644 views

I want the function that defines truncated lognormal distribution

Problem, I have a process(water level in chamber), it perfectly fits with lognormal. But the chamber has a maximum water level, after which no effect of water must be there. I guess I can use the ...
user avatar
5 votes
1 answer
479 views

random number generation of truncated multivariate normal distribution

I want to generate random numbers from truncated multivariate normal distribution specified as follows: $ \begin{bmatrix} Y \\ X \end{bmatrix} \sim N \begin{pmatrix} \begin{bmatrix} \mu_Y \\ \mu_X \...
user0131's user avatar
  • 357
0 votes
1 answer
148 views

Maximum likelihood fit of left truncated Weibull distribution

I want to fit some samples to the right tail of a Weibull distribution. To fix the notation: the samples are $\{X_i\}_{i=1,\ldots,n}$, all samples are greater than a fixed threshold $L$, the $X_i$'...
AndreA's user avatar
  • 225
0 votes
0 answers
43 views

How to choose priors for bounds on circular truncated distributions?

I am considering choices of priors for truncated distributions on a circle. Let's take the truncated normal distribution on the unit circle as an example. It has parameters $\mu \in [-\pi, \pi]$ and $\...
Galen's user avatar
  • 8,125
0 votes
0 answers
113 views

Left censored regression bounded at zero

I've been handed some data that is obviously left-censored. Many zeroes, probably due to insensitivity of the assay. However, since it is a protein level assay, it is theoretically impossible for any ...
Bryan's user avatar
  • 1,190
2 votes
1 answer
87 views

Sufficiency and completeness of truncated distribution

[From Theory of Point Estimation (Lehmann and Casella, 1999, Exercise 6.37)] Let $P=\{P_\theta:\theta \in \Theta\}$ be a family of probability distributions and assume that $P_\theta$ has pdf $p_\...
WinnieXi's user avatar
2 votes
1 answer
102 views

Is the truncated squared expected value less than the variance?

Let the continuous random variable $X$ be distributed with mean $\mu_x$ and variance $\sigma^2_x$ with support $[0, \infty]$. Let the random variable $Y$ be the right truncation of $X$, with ...
GCru's user avatar
  • 225
3 votes
0 answers
501 views

Fitting truncated and censored data

I have data that is truncated on the left and censored on the right. The reason is that this is claims data, which for a claim gives the amount of the claim. The claim appears in the data: Only if it ...
Meth's user avatar
  • 131
4 votes
1 answer
105 views

Is the mean of the left-truncated binomial distribution convex in p?

The expectation of the binomial distribution of successes in $G$ trials, left-truncated at $R$, with success probability $p$, is $$ E[X|p] = \frac{\sum_{l=R}^Gl\phi(l)}{\sum_{l=R}^G\phi(l)} $$ where $$...
dash2's user avatar
  • 235
0 votes
0 answers
104 views

Back Transformed Truncated Negative Binomial Model Results Less Than One

I'm using a truncated negative binomial model to describe my count data where all values are >=1. I have attempted to back-transform my model results using emmeans. However, all of my back ...
user364517's user avatar
3 votes
1 answer
345 views

Generate a truncated lognormal distribution given mean, variance, lower bound and upper bound?

Basically, I would like to generate a sample of truncated lognormal distribution given mean, variance, lower bound and upper bound. Note that the mean and variance here are the mean and variance of ...
Hongbo W's user avatar
0 votes
0 answers
29 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 ...
user101874's user avatar
1 vote
0 answers
41 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 $k$: $...
dash2's user avatar
  • 235
2 votes
1 answer
352 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 ...
gregorp's user avatar
  • 371
1 vote
1 answer
184 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 $...
GiulioGCantone's user avatar
2 votes
0 answers
142 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 ...
half-pass's user avatar
  • 3,731
0 votes
1 answer
313 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 ...
Jeff's user avatar
  • 165
3 votes
2 answers
1k 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 ...
Uk rain troll's user avatar
2 votes
1 answer
341 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}\...
Tingchang Yin's user avatar
1 vote
0 answers
54 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 } ...
Pro Q's user avatar
  • 697
1 vote
2 answers
356 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) ...
Tingchang Yin's user avatar
1 vote
0 answers
58 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 ...
samsambakster's user avatar
7 votes
1 answer
2k 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, \...
Adrian's user avatar
  • 2,839
2 votes
1 answer
71 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 ...
Arnaud Mortier's user avatar
0 votes
0 answers
128 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 ...
user112495's user avatar
0 votes
0 answers
133 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 ...
Nuket Ipek Cetin's user avatar
1 vote
0 answers
554 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 ...
Joe's user avatar
  • 11
2 votes
0 answers
140 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 $E_{A}[x | x \leq t] \geq E_{B}[x | x \leq t]$, ...
user313975's user avatar
3 votes
0 answers
51 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 ...
user312267's user avatar
8 votes
2 answers
5k 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}{\...
Herpes Free Engineer's user avatar
3 votes
1 answer
107 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 $X$?
AnonA's user avatar
  • 93
1 vote
1 answer
411 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, ...
BelwarDissengulp's user avatar
1 vote
1 answer
678 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 ...
monade's user avatar
  • 509
2 votes
0 answers
56 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 ...
Dave Bapst's user avatar
1 vote
0 answers
236 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 ...
Kcoblentz's user avatar
2 votes
2 answers
1k 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?
M N's user avatar
  • 63
4 votes
1 answer
638 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?
M N's user avatar
  • 63