# 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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### 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 ...
1 vote
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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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I'm trying to understand survival analysis better and ran into a weird problem with hazard rates - when I calculate it by hand, i.e. with $$h(t) = \left( \frac{ P(T \leq t + \Delta t) - P(T \leq t)}{... 1 vote 1 answer 80 views ### How to estimate the variance covariance matrix of a Weibull survival model manually? In flexsurv the var-covar matrix of the parameters can be produced with the vcov() function. This will produce a var-ovar matrix for the shape and scale parameters provided by the function coef(). ... • 151 0 votes 0 answers 126 views ### How to prove the MLE for Weibull distribution is biased or unbiased? My attempt is like this: Let X \sim \text{Weibull}(\alpha, \lambda) be a random variable following a Weibull distribution with pdf fx(x; \lambda) = \begin{cases} {\alpha}{\lambda^{-\alpha}} x^{\... 0 votes 1 answer 69 views ### Extended Weibull-Cox model survival function I'm reading an article where the authors use an extended Cox-Weibull hazard model with time-varying covariates to model survival time of an individual. This individual is allowed to start at week m, ... • 337 1 vote 0 answers 98 views ### What is the motivation behind the inverse Weibull distribution It seems like both the Weibull and the inverse or reversed Weibull model failure rates, waiting times and extreme phenomena. The inverse Weibull pdf is$$f_X(x; \alpha, \beta) = \beta \alpha^{-\beta}x^... 227 views

### 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] 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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### Is there an analytical equation for the uncertainty in an estimate of Weibull Modulus?

If I have a sample of $N$ measurements that follow a two-parameter Weibull distribution, how does the uncertainty in the estimate of the shape parameter (Weibull modulus, $k$) vary with $N$? I've done ...
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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 ...
1 vote
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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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### Component reliability with an uncertain starting time

I have a lab data analysis challenge which I think can be viewed as a kind of reliability analysis problem. Imagine a warehouse is filled with light bulbs that were installed at some unknown times in ...
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### Are there any Python packages which can fit Conditional Weibull Distributions

I'm trying to fit failure data which already has a burn in time, and Im in need to use the Conditional Weibull Distribution. Are there any Python packages which have this distribution implemented?
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### Why do our devices fail?

I would like to figure out why some devices of my company fail. Therefore, I'm able to use a list in which around 300 devices are listed together with about 70 parameters while only half of it is ...
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### Predicting time to event / duration data

I've built a parametric survival model (survreg in R) to predict injury recovery duration using features such as age and treatments. I'm looking at trying model-based boosting using mboost with ...
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### How to find shape and scale parameters for a Weibull distribution in survival analysis

I am to run a superiority clinical trial and I want to fit a parametric model under the Weibull Distribution. But I am confused about how should I find the shape and scale parameters for the Weibull ...
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### Weibull and Lognormal Fits

I have simulated failure time data for some components. I tested whether a Weibull or lognormal distribution best fit the data. Please see Figures below. The figures provide median and $95\%$ ...
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### Estimating Right Censored Data

I'm a newbie at Math, and I am just getting my feet wet when it comes to understanding math and statistics so please forgive my ignorance or question if it's already been answered or if materials are ...
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### Decay function (e.g. weibull?) with numeric (i.e. not survival analysis) data

An example data frame: ...
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### Predict based on time using a weibull

Example data with weibull decay for growth: ...
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### Weibull plot to assess goodness of fit

I would like show whether my data fit a Weibull distribution. What kinds of graph should I plot? Is the following graph appropriate one and what is this called? How can I plot it in R?
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### Interpretation of Weibull Survival Time Prediction from a Survreg Object

Code is somewhat like this: ...
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### Test whether two separate Weibull distributions describe the data better than a single Weibull distribution

My question is very similar to this one, but with the Weibull distribution replacing the Poisson distribution. Let's say I am analyzing the distribution of times between failures for an engine, with ...
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### Understanding the probability distributions behind a Monte Carlo experiment

A colleague and I are trying to model the expected maintenance cost/h (E[C/h]) of a component A on an aircraft over its life based on its reliability distribution. As the component fail, it's replaced ...
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### Predicting survival/event probability with multi-level Weibull model and time-dependent covariates

I am still a beginner when it comes to survival analysis. I have fitted a parametric (Weibull) survival regression model with time-dependent covariates using the R package flexsurv via: ...
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$\newcommand{\szdp}{\!\left(#1\right)} \newcommand{\szdb}{\!\left[#1\right]}$ Problem Statement: Let $Y_1,\dots,Y_n$ be a random sample from the probability density function given by f(y|\...