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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64 views

Weibull probability Plot?

I am trying to reproduce a plot from a paper. The plot is a Weibull probability plot and is used to illustrate why a Weibull distribution is appropriate for modelling failure times. The plot is ...
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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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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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110 views

Why should there be two solutions for each parameter of likelihood ratio equation for Weibull-distribution?

I try to calculate the confidence ínterval of a Weibull distribution by means of the Likelihood method as described in ReliaWiki. In order to find the confidence intervals, I have to solve the ...
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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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28 views

survival model with weibull sojourn time in R

I aims to develop multi state survival model in R with the transition time between any two states follows Weibull distribution. However, based on the documentation and as shown in the picture below, I ...
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45 views

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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What data to include in Weibull fit

I have a set of inspection data that I want to fit to a weibull distribution to understand whether further inspection would provide much value. For example, I have 2000 items of which we have ...
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1answer
49 views

A goodness of fit test for the Weibull distribution

I have data which I have to test to see if it comes from the Weibull distribution. I don't know the parameters so I am looking for a goodness of fit test (like the Lillefors test), preferably which I ...
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46 views

Weibull Model in Stata vs R

I am currently trying to replicate a study on war duration, which used Stata's streg function to estimate a parametric Weibull model. The stata code reads: ...
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Predicting survival probability at a future time for proportional hazard model

I have a Weibull proportional hazard model with fitted parameters $\lambda$ and $k$ and a time dependent covariate $x(t)$ with fitted coefficient $\beta$, such that the hazard function is given by, $...
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Weibull Stats for Testing Significance of Ultimate Strength in Mechanical Failure

First, I'll start with some background that may explain the ignorance that will likely be encountered in the remainder of the post. I am an archaeologist attempting to study the flexural strength of ...
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1answer
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Estimating two-component mixture of Weibull distributions?

Is there any existing package (preferably in Python or Matlab) to estimate the parameters of a two-component Weibull mixture model? And failing that, I am hoping to get some pointers towards rolling ...
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Weibull Distribution with priors on shape and scale diverges

I have a variable that is Weibull Distributed Duration ~ dweib(Shape,Scale) The Shape and Scale parameters are distributed to log-normal and Weibull ...
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1answer
179 views

Prediction of regression coefficients with XGBoost

I am doing survival analysis. There is a dataset of items (id, group_id, observed lifetime, censorship status), each item belongs to a certain group. Each item is ...
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1answer
64 views

Validity of Weibull distribution [closed]

I have come across validation engineers picking the Weibull distribution as a way to generate test stimulus. When they do this, they seem to chose the parameterisation without reference to any ...
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1answer
24 views

Reliability Testing, Determining Weibull parameters

I want to use a Weibull analysis for demonstrating the reliability of a piece of equipment that will be set to cycle. How do I select the proper scale and shape parameters for the distribution if I ...
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Full-parametric Weibull accelerated failure time model using deep-learning library Keras

I wonder if it is possible to fit a full parametric AFT model with the deep-learning library keras. My AFT model assumes that survival function is influenced by some covariate specific acceleration ...
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1answer
85 views

Prediction interval for a Weibull distribution

Suppose I am producing units and have tested the failure time of some proportion of them (say 10%), possibly with some right censoring if they didn't fail within the testing period. I'm able to fit a ...
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Prove that bias of MLE for Weibull process

In the case of fixed observation interval $[0,T]$ of a Weibull process, I learned that the MLE of the shape parameter $\beta$ and MLE of the scale parameter $\alpha$ are as follow: $$\frac{1}{\hat{\...
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42 views

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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36 views

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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111 views

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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130 views

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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9 views

What's a simple explanation for risk and its formula in survival analysis, weibull regression

I have that if the model is $\ln(\mu_i) = \beta_0 + \beta_1 x_1$ where $x_1 \in \{0,1\}$ and represents tired (or anything suitable, sex, etc). The model also has a shape parameter, $\gamma$. ...
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274 views

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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54 views

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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1answer
245 views

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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How do I estimate parameters of Weibull distribution in R based on a given dataset? [duplicate]

Here I got the Weibull distribution function like this, and how can I estimate the parameters by the below data set?
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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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1answer
56 views

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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50 views

Comparison between cumulative and weibull method for MTBF

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1answer
379 views

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 $\lambda,k > 0$...
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Weibull coefficients comparison [closed]

I´ve 838 sets of data that represents points distributed by height. Those that can be fitted by Weibull function. So, I normalized them and adjusted the corresponding distribution function, saving it´...
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12 views

Duration Analysis with Clumping at Infinity?

I am currently trying to build a model to analyze how price setting today affects how long it takes for a customer to return. My first cut was to fit a Weibull regression where the log of the scale ...
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1answer
43 views

Predicting survival time from log-hazard

I have estimated a Weibull regression model in BUGS/JAGS which gives me the log-hazard as a function of intercept (baseline hazard) and covariate effects. The intercept is estimated as -9.826 and one ...
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299 views

What is the Most Probable Maximum for a Weibull distribution?

The title says most of it. I have a signal from which I need to calculate the most probable maximum extreme value. The approaches I have so far are: Assuming a Gaussian process, fit a Rayleigh ...
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121 views

Proof of alternative parameterization of Weibull Survival Model

In Parametric Survival Models by German Rodrıguez (hyperlink at bottom), it is stated the Exponential and Weibull models can be parameterized in a linear form (with time parameterized as $\log(T)$). ...
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1answer
99 views

Hazard function for a growing population

I want to model the expected failure rate in a growing population. Each individual has a high infant mortality (e.g. Weibull(shape=0.5, scale=100)). So the ...
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1answer
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Sensitivity of Weibull survival model to early missing data

I have a few datasets of survival times that appears to be very well-modelled by Weibull distributions; I am mostly interested in whether $k$ is above, below or around 1. However, there is a real ...
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1answer
135 views

fitting weibull distribution to “wind speed” data

I am trying to fit a weibull distribution to my wind speed data with the following code: fitdistr(av_ws, densfun = "weibull") #av_ws is the wind speed data 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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Moment generating function of a Weibull distribution and root finding heavy and light tailed case

I consider the equation $M_x(v)=1+(1+\beta)\mu$ and I need to find the solution $v>0$ such that the equation is fulfilled. For this example I consider the moment generating function $M_X(v)$ of a ...
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138 views

Weibull distribution is not a glm, why? [duplicate]

It is a generalized linear model with a linear combination of covariates related to the response via a canonical link function. Why weibull distribution is not a glm?
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Fisher information matrix in logistic regression

I am self-studying the basics of logistic regression. I came across this sentence: In logistic regression expected and observed information matrixes are equal I am aware that the information ...