# 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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### Surpyval Weibull goodness of fit

I have been using surpyval to fit some calibration data to a weibull distribution. I would like to assess the goodness of fit but I am not sure how to approach this. I had previously used "...
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### How to handle intermediate observations in Weibull Models (censoring)

I'm currently working on updating previously created Weibull Models on component failure. The Situation: I have data available, that shows if a component of a machine has been exchanged (mainly ...
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### Assessing whether a dataset follows a distribution using Q-Q Plot

I recently found myself answering a question on Stack Overflow about adjusting a dataset to a unknown distribution. Adding my two cents to the community, I have provided a script to draw a Q-Q Plot in ...
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### Inconsistent posterior from hierarchical survival model

I asked about this question on Stan forum but no one replied so dual posting here. I'd really appreciate some insight, as I'm completely stuck. I’m trying to do hierarchical survival modeling using ...
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### Weibull distribution: Is it possible to solve for the shape and scale from the mean?

I'm modeling product lifetimes. If I know what I want the average lifetime of a product in my model to be, is it possible to fit a Weibull distribution to only that data point?
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### Capture time variation in survival analysis

I am currently working with intraday time-to-event data, where the time to event typically spans just a few minutes. I want to compare the survival curves of two subpopulations in my sample. The ...
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### What is the right Haar prior for the Weibull distribution?

From Wikipedia, the Weibull distribution is defined with the exceedance distribution function (aka survival function) $\exp[-(x/\lambda)^k]$. If I transform the random variable $x$ using $x'=ax^b$ ...
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### DIfference between hazard ratio and partial hazard in survival analysis

The hazard function in survival analysis is represented as (https://in.mathworks.com/help/stats/cox-proportional-hazard-regression.html): Here the exponential term is termed as hazard ratio as ...
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### Deriving the distribution of $X^p$ if $X$ is Weibull distributed and estimating the parameters

I am stuck with the following problem and hope somebody can help spotting the error. I am not sure if it's a simple math or programming glimbse or whether the issue is more complex (e.g. concerning ...
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### Logic to caluclate shape and scale parameter in survival analysis

I have the below dataset: ...
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### Maximum Likelihood Estimator Multiple Parameters

Question Suppose two groups on treatment and can be modelled by a Weibull distribution with a normal probability density function \begin{align} f(x; \alpha, \lambda) = \alpha \lambda x^{\alpha - 1}...
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### Why does the best fitting Weibull distribution for this survival data deviate further from the actual data than a poorly fit distribution?

I started working with the Gumbel distribution and fit it to the lung dataset to try it out. I then compared it with the survival curve using the Weibull ...
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### How to assign reasonable scale parameters to randomly generated intercepts for the Weibull distribution?

This is a follow-on to post Correctly simulating an extreme value distribution for survival analysis?, as I work towards adaptation of that code to the Weibull distribution. In the below code I ...
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### How to generate random values representing lognormal parameters for simulating the lognormal distribution using survival data in R?

I am trying to generate random parameters for the lognormal distribution in order to test parameter sensitivity and for simulating (predicting) future survival rates, using the ...
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### How can I fit a distribution to a dataset while forcing it through an exact point in r?

This code was kindly recommended to me in my original question. It returned the same parameter estimates as the software called CRAFT by Aon Benfield. I have also managed to replicate it for the ...
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### Options for transforming the variance-covariance matrix generated by the survreg() function to the original scale of the Weibull distribution?

I'm working with the survreg() function of the R survival package, and I understand that the default scale parameter for the ...
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### Is this an adequate example for simulation and modeling uncertainty in survival and hazard curve estimates?

I'm studying simulation and in particular uncertainty in survival curve estimates, by drawing from a distribution of parameters (for the Weibull distribution), using the variance-covariance matrix ...
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### Why am I not able to correctly calculate the median survival time for the Weibull distribution?

The survival function for the Weibull distribution is: $S(t) = exp(-\lambda t^\alpha)$, $\lambda$ = scale parameter, $\alpha$ = shape parameter If I wanted to calculate the median survival time, I ...
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### What is the minimum of 2 Weibull distributions with the same shape parameter

If X and Y are two independent Weibull distributions with the same shape parameter, what distribution is the min(X, Y). I am trying to find out the hazard ratio for the following case. If I model Z=...
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### How to simulate right-censored Weibull PH survival times with time-varying covariate?

I am trying to simulate data coming from a joint model of longitudinal and survival data. Basically, my thought process is this. I need to define a maximum follow-up time, F. I need to define ...
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### Interpreting shape and rate parameters from a weibull model of mortality hazard in BaSTA

I am using the BaSTA package in R to estimate sex differences in survival parameters for a capture-recapture dataset. When I use a simple Gompertz model the parameters are very interpretable (b0 ...
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### Obtain the survival function plot by building an overall survival regression model

I need to build an overall survival regression model that can show the survival plots for id's with multiple rows. I have used the Weibull function to define the baseline hazard function h0(t) and Cox ...
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### 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 $X_i$'...
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### Calculate survival function for remaining life prediction using CoxTimeVaryingFitter in Python

Cox’s time-varying hazard model is given here which is "CoxTimeVaryingFitter" The mathematical formulation is represented as: The values of log partial hazards "(x−x¯)′β" are ...
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### Calcuate the coefficients of time varying covariates in Cox hazard model

The cox time varying covariates (x(t)) model is as such: The above formulation can be seen here: https://lifelines.readthedocs.io/en/latest/fitters/regression/CoxTimeVaryingFitter.html Here, can ...
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### Showing suspended (right-censored) data points in diagram (distributed on x-axis)

How is it possible to show the suspended (right-censored) datapoints (distributed on x-axis without value for y-axis) in e.g. Probability Plot - Weibull CDF like the green triangles in attached image?
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### Mean Residual Life of Weibull Distribution closed form

Weibull distribution function is parameterized as $F(x) = 1 - e^{(-(x/\sigma)^a)}$ and survival function is $S(x)= e^{(-(x/\sigma)^a)}$ where $a$ is shape parameter and $\sigma$ is the scale ...
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### Weibull distribution parameterization

I have the following Weibull distribution: $f(x;\lambda,\beta) = (\lambda\beta)x^{(\beta-1)}e^{(-\lambda x^b)}$ where $\lambda$ is scale parameter and $\beta$ is shape parameter. I have an ...
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### How to calculate confidence intervall and z-score for a weibull distribution? (2 and 3 parameter)

How can i calculate the confidence interval (CI) of a weibull distribution? I have raw data e.g.: 3,5,7,2,11,97, 223, ... I can calculate the mean (µ), standard deviation (SD). But how can i ...
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### UMP Test and UMVUE when there are nuisance parameters

Consider $X_1,...,X_n \sim Weibull(\theta, c)$ where $c>0$ is unknown. Several textbook examples consider when $c$ is known, but here, we consider when $c$ is unknown. Suppose now we wanted to find ...
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### Distribution is Weibull but variable diagnostics lines cross and converge - what to do?

Reproducible data: ...
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### Finding shape and scale parameters of gamma distribution

I have a dataset [click here][1] and trying to find the shape and scale parameters of gamma distribution. ...
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### Find extreme values in relative frequencies

I have the relative frequencies of elements in roughly 450 samples (with varying sample sizes). These elements are organisms in fecal samples. I am interested in finding extreme values of these ...
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### What are the operational links between exponential and weibull distribution

I recently read a very interesting article about competing risks that came with simulations. In these, the author defines a Weibull distributed variable w using an ...
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### What is the meaning of the flexsurvreg plot and its res.t?

I use the flexsurverg to estimate the a Weibull survival model with a time varied covariate, where “utility” is a continuous function, and the result is shown as follows: I plot the fit function and ...
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### AFT model interpretation

I am slightly confused about the way accelerated failure time models work in comparison to proportional hazard models. Is it a correct statement that while the PH model assumes covariates multiply ...
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### Universal Approximation Capabilities of Mixture of Weibulls

Can a mixture of $N$ Weibull distributions approximate any continuous density with non-negative support, if $N$ is sufficiently large? (If so, a reference to the proof would be greatly appreciated). (...
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### Finding Variance of Proportional Hazards Regression Coefficient Estimates in Weibull Regression

So I am doing Weibull regression in R with the exponential relative risk function. The proportional hazards model formulation assumes that the hazard rate is given by \alpha(t;a,\sigma, \boldsymbol ...
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### Predicting failure (e.g. from weibull) of part that has already survived a certain time

Simple question, but I'm overthinking it. Say that I already have a cumulative failure distribution, cdf, (Weibull, but let's just assume any type of distribution) calculated from historical part data....
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### How to calculate Weibull confidence interval using chi-square distribution?

I have a dataset, which I assume has a weibull distribution : ...
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### Lifetime estimation - Weibull vs Survival

Survival analysis is mainly about estimating the lifetime of nearly anything or even anything: And Weibull analysis is also about estimating the lifetime: How are they different (in general) and ...
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