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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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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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Survival regression on an interval

I am experimenting with survival regressions (like weibull) on on interval of a data. For instance, if I use the lung data in R I want to use the data in a certain ...
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Semi Markov Process for different condition states of a bridge

Following case: I have bridges in different condition states from 1 to 4 (good condition to worse). For every condition I estimated the weibull parameters form the data I got from an inspection (there ...
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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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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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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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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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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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166 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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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 $\lambda,k > 0$...
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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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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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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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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: 1- Assuming a Gaussian process, fit a Rayleigh ...
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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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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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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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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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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 ...
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How to prove the existence of upper truncated point?

Currently I am working on a data-set seems to have a Weibull distribution. Problem is that not sure if Weibull or Truncated-Weibull is better to use. Any methods or Hypothesis test there to prove if ...
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Independent variables in truncated Weibull distribution

I am relative new to statistics and currently working on a problem about crash rate analysis. It is appears to be a zero-inflated scenario, then I decide to use the hurdle model. The first part will ...
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Attempting to find mean of Weibull function in R

I am using a Weibull distribution in R, and know that: E(X) = 1000 and Var(X) = 500,000 Knowing: E(X^r) = ($\Gamma$(1+ (r/$\gamma$))) * 1/c^(r/$\gamma$)) I ...
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Why don't I see my points on cullen and frey graph

I have a set of data of 5 members. based on some previous questions , I was expecting to see where my actual points are located on the graph. in my case I see the theoretical but not my points. just ...
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Getting weirdly small cdf and pdf values for a set of data of 5 members in R

I am doing a Weibull and normal distribution analysis for a set of my data which are : 336256 620316 958846 1007830 1080401 So to avoid putting the whole code here, I refer you directly to the ...
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Why is Hazard Function called rate of failure?

I am confused why Hazard Function is called rate of failure. Here is what I understood about Hazard Function. Suppose we are dealing with Weibull and let $f(X)$ be the pdf, $F(X)$ be the cdf. Now, I ...
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Distribution of maximum over minimum of Weibull(alpha, 1)

Let the PDF of Weibull $(\alpha, 1)$ be $$ f_X (x) = \alpha x^{\alpha-1} \exp\left( - x^{\alpha}\right) $$ I know from probability integral transfrom that $$ X_{(1)}^{\alpha} \overset{d}{=} Z_{(1)...
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$\mathbb{E}(\log(X_{max}/X_{min}) )$ of Weibull(alpha, 1)

I'm trying to find the expectation of log(max/min) from n samples of Weibull(alpha, 1). But I keep failing. Can anybody give some hints? I tried: $\mathbb{E}(\log(X_{max}/X_{min}) ) = \int_0^{\...
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Why are Weibull Results Different in R than in Stata?

I'm working with a time-series dataset that looks like the following: I want to run a survival model with a weibull parametrization, but I'm getting different results in Stata and in R. In Stata, ...
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60 views

fitting distribution to values (some of which are negative)

I'd like to fit a distribution. ...
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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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Marginal density of $X_1$ given that $X_1 + X_2 = d$ where $X_1$ and $X_2$ are iid Weibull?

In their tutorial (page 23) on heavy-tailed distributions, Nair et al. present the following graph (taken from a pre-publication chapter from a book by the same authors): Pictured are the marginal ...
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How to calculate mortality rate or probability of death at time t for various parametric distributions, e.g. Weibull, exponential, log-normal

If I have lambda and gamma, can I estimate that the probability of death at time t, based on a Weibull distribution is: What are similar formulas for the exponential, Gompertz, log-normal, log-...
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Why isn't Weibull Maximum Likelihood Estimation possible with x=0?

As everybody knows, the pdf of the Weibull distribution is defined by $ f(x)= \left(\dfrac{a}{b}\right)\left(\dfrac{x}{b}\right)^{a-1}exp\left(-\left(\dfrac{x}{b}\right)^a\right)\quad \text{for } x \...