# Questions tagged [weibull]

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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### 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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### Generating Failure / Suspension data from Weibull Distribution

I've been trying to make some synthetic failure data in MATLAB and I'm coming across an issue when I try to refit the Weibull distribution from my synthetic data. For example, assuming a Weibull ...
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### Using R to maximize a two parameter Weibull model via multivariate extension of Newton-Raphson method

I am just getting back into using R for the first time in a while, and wrote some code to perform the aforementioned task in the title. I was wondering if anyone could take a look at it and see if ...
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### distribution for scaled Maximum of n independent Weibulls for $n \to \infty$

Assume that $X_1, X_2,...\sim Weibull(\lambda, k) \quad iid.$, i.e. $F(X_1\leq x) = 1-e^{-(\lambda x)^k}$ define $M_n:= \max\{X_1, ..., X_n\}$ and $\tilde{M}_n:=\frac{M_n-b_n}{a_n}$ according to ...
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### Fitting Probability Distribution to Failure Data with discrete, right censored stress

I'm a bit unfamiliar with survival analysis and I'm struggling to find examples of the particular problem I wish to tackle (which I don't think is particularly unique actually). Imagine I'm doing a ...
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### cumulative distribution function for non-normal distribution

From this article, I read that the author drew four versions of CDFs each plotted in different distributions (all four plots come from the same sample data) From these four plots, the author chooses ...
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### R - nlm and Weibull Maximum Likelihood

Good day, I am working on an assignment where I have to Calculate the maximum likelihood estimates of $\alpha$ and $\lambda$ along with their standard erorrs on the basis of an independent and ...
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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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### R - how to estimate shape and scale parameters of Weibull distribution for claims development factors

I have a set of insurance data. Development factors fall with period, so follow Weibull distribution. I want to estimate Weibull parameters and smooth Development Factors. If I estimate parameters of ...
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### Generating Correlated Random Variables following Weibull Distribution

I am working on analyzing power generation from geographically distributed wind farms. I have wind speed data that have been collected at multiple locations, but the measurement periods for different ...
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### Mean Survival Time Under Weibull Model Using survreg

Under the Weibull parametric model, we assume the survival time $T \sim \text{Weibull}(\alpha, \lambda)$, with density $f_T(t) = \alpha \lambda (\lambda t)^{\alpha - 1} \exp(-(\lambda t)^\alpha)$. ...
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### Which variables in the models below meet acceptable thresholds for accuracy, also, which model is more statically accurate

Which variables are most significant? ...
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### In a time to event analysis, when is it appropriate to use parametric models to compute restricted means?

Restricted mean is gaining popularity as a substitute for the hazard ratios to compare survival times in time-to-event analysis, especially in observational studies where chances of violation of ...
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### MLE of Weibull in the context of Survival analysis

I have the following likelihood (Weibull model with parameter $\alpha, \lambda$), and I would like to maximize it with respect to $\alpha, \lambda$.  \begin{aligned} L (\alpha, \lambda; t, \delta) ...
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### How to generate a Weibull distribution with inverse transform

Given $X\sim \text{Weibull}(\lambda,k)$, generate samples from the Weibull distribution using the inverse transform. We know $F_X(x) = 1-\text{e}^{-(x/\lambda)^k}$ for $x\ge 0$ with $\lambda,k > 0$...