# Questions tagged [weibull-distribution]

The Weibull distribution is a probability distribution with applications in survival analysis, reliability engineering, failure analysis, industrial engineering, extreme value theory, weather forecasting, forestry, and more.

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### asymptotic unbiasedness of weibull mle

It's known that the MLEs of the two-parameter Weibull distribution scale and shape parameters are not available in a closed form. It is, however, known that they do exist, are unique, and moreover, ...
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### Conjugate of Weibull with shape known

This isn't exactly a homework problem but rather a self-selected problem I'm doing to prepare for a midterm. I can see from Wikipedia that it is an inverse gamma but I am unable to reach the ...
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### How can I compare parametric and semiparametric survival models?

On a given dataset, I am running a semiprametric Cox proportional hazards model, together with a series of parametric models (Weibul, gamma, lognormal, exponential, etc.). How can I know which is ...
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### Weibull Distribution v/s Beta Distribution

I've recently fallen in love with the Weibull Distribution and have gotten a reason to see if there's a mapping of this distribution to an interval (0,1). After plotting the Beta Distribution against ...
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### What methods are there for estimating distributions based on histograms?

I recently worked on a consulting project where a client wanted to estimate gamma and weibull distributions based purely on histograms rather than raw-data. I have never worked with problems like that ...
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### How are the Rayleigh Distribution and Weibull Distribution related?

I am trying to work out a physically intuitive way of understanding how the Weibull arises. Also according to the Wikipedia entry on the Weibull distribution, there is some how a relation to the ...
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### Posterior distribution for Weibull scale parameter with censored data

I am modeling a survival problem using a Weibull distribution with known shape parameter $k$ and unknown scale parameter $\theta$. The PDF and CDF are given by, \begin{align} f(t|k,\theta)=\frac{k}{\...
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### Convergence rate of the maximum of Weibull random variables to a Gumbel distribution

Given a sequence of iid samples $X_1, \dots, X_n,$ where each $X_i$ comes from a Weibull distribution with shape parameter $k$ and scale parameter $\lambda$. Then it is a well-known result that the ...
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### Confidence bounds for Weibull MTTF

I have three times-to-failure (TTFs) as 28, 40, 43. I fit a Weibull distribution on the data, and want to calculate a 95% confidence interval for the mean-time-to-failure (MTTF). Using ...
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### Weibull regression sensitive to scaling of predictors?

I'm running a Weibull regression and decided to simulate data to assure myself that the model is able to recover the true parameters. ...
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### Detect the correct distribution from a small sample size by using fitdistrplus in R

The simplest version of the issue that I am looking for help is: How to detect the correct distribution from a small sample size in R by using fitdistrplus A simpler version: I am generating some ...
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### Monte Carlo simulation for fitting distributions (Weibull and log-normal)

I am working on a computer project which needs statistical analysis and I am not much of a statistic person. I have a Bluetooth (BT) detector device which detects passing Bluetooth devices (i.e one ...
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### Likelihood function for a Weibull model

I have an assignment for my course Microeconometrics. Currently I am stuck on the following question You are asked to help out with the statistics of a medical study. We are interested in the time ...
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### Confidence intervals for extreme value distributions

I have wind data that i'm using to perform extreme value analysis (calculate return levels). I'm using R with packages 'evd', 'extRemes' and 'ismev'. I'm fitting GEV, Gumbel and Weibull distributions,...
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### Accelerated Failure Time scale parameter excessively large when data is right censored

I am using an accelerated failure time model with the Weibull distribution to predict failure times. My failure times range from 1 - 365, with many (80%) data points that are right censored (no ...
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### Likelihood ratio test Weibull distributed r.v -- problem calculating the critical region

Let $X$ be a r.v which is Weibull distributed with $k=4$ and $\lambda>0$. I'm looking at the following test: \begin{align*} H_0:\lambda &= 1\\ H_1: \lambda&\not = 1. \end{align*} I have ...
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### Testing for Constant Hazard Function

My colleagues and I have some unemployment data, and we'd like to test the hypothesis that it's drawn from a memoryless distribution (= constant hazard function). Is there a standard test for this? (...
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### Weibull distribution fit

I have a random variable $X$ for which it is known a priori that $P(X > x) = \exp(-ax^b)$, i.e. the CDF is given by $F_X(x) = 1-\exp(-ax^b)$. I would like to determine the values of $a$ and $b$ ...
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