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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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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Characteristic function of Weibull distribution

I am recently learning about characteristic functions. I find them very interesting, but I seem to be misunderstanding something. Wikipedia claims that they are the Fourier transform of the ...
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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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Weibull Proportional Hazard in pymc

I’m looking to create a Bayesian proportional hazard model where the baseline hazard is modeled by a Weibull distribution (or some similar continuous distribution). I’ve reviewed (and implemented) the ...
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Identify / separate sorts of failure

I ran a Weibull analysis on data of devices which consists mainly of failures over time (80 % died, 20 % are still alive). In total there are around ~4500 devices. After conducting this analysis I ...
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Is a radioactive process describable by survival analysis?

According to this source, the survival function is defined as $ S(t) = e^{- \lambda \cdot t} $ while, according to this source, the number at time $ t $ of radioactive atoms is $ N(t) = N_0 \cdot e^{- ...
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Schoenfeld residuals - theoretical question

I have a doubt about the Schoenfeld residuals that are used to check the Cox proportional hazard model. The residuals formula is: $$\hat{r}_{ik}=c_i(x_{ik}-\hat{\bar{x}}_{w_ik})$$ $$\hat{\bar{x}}_{...
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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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Compare quality of fit, MLE vs method of moments

I have many different datasets that presumably should follow the same distribution type (but with distinct parameters). I've identified one distribution type that seems to describe best the data (...
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Variational Autoencoder with Dirichlet distributed latent space using the Weibull Distribution

My goal is to create an VAE with an Dirichlet distributed latent space. Since the reparametrization trick does not work for the Dirichlet Distribution, I am trying to approximate the Gamma ...
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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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Finding the inputs and outputs of a Weibull distribution

If I have a Weibull distribution with a CDF of: $P_\theta (\lambda ,k) = (\frac{k}{\lambda })(\frac{x_i}{\lambda})e^{-(\frac{x_i}{\lambda})^k}$ for $x_i > 0$ And a MSE of: $J_{\lambda ,k}(x) = \...
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Can we force a fitted distribution to have the same mean as the data?

I have some rainfall data that I am fitting with a Weibull distribution. The mean of the rainfall data is 0.62, but the mean of the best-fit Weibull distribution is 0.69. As a result, when I simulate ...
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Finding a distribution of Accelerated Failure Model

Can someone please answer these 3 questions related to AFT model? In Accelerated Failure Time (AFT) model, $S(t│β,x)=S_0 (exp(β^T x).t)$, where $S_0$ is the baseline survival function, does $S_0$ ...
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Conjugate Prior for Alpha Power Inverse Weibull Distribution

Let $X$ has Alpha Power Inverse Weibull (APIW) distribution with pdf $f(x) = \frac{\log \alpha}{\alpha - 1} \lambda \beta x^{-(\beta+1)} e^{-\lambda x^{-\beta}} \alpha^{e^{-\lambda x^{-\beta}}}, \; x&...
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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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Uniformly Most Powerful Test for Weibull Distribution

$\newcommand{\szdp}[1]{\!\left(#1\right)} \newcommand{\szdb}[1]{\!\left[#1\right]}$ Problem Statement: Let $Y_1,\dots,Y_n$ be a random sample from the probability density function given by $$f(y|\...
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Is there a "Weibullity" test?

There exist several tests of normality. This is, tests for checking if a data set is normally distributed. Is there a "Test of Weibullity"? This is, a test for checking if a data set is ...
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Conditional distribution using Gamma and Weibull

I'm trying to compute the conditional distribution of $X|Y = y$. $X\sim Gamma(3,2)$ $Y|X = x \sim Weibull(2,x)$ I was doing this: $f_{X|Y = y}(x) \propto f_x(x)\cdot f_{Y|X = x}(y)$ $f_x(x) = \frac{1}{...
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Power Generalized Weibull (PGW) Distribution

I'm trying to understand Power Generalized Weibull (PGW) distribution for my final project. PGW distribution is the generalization of Weibull distribution. The cdf of PGW distribution is $G(x) = 1 - e^...
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Simulate from Circular - Linear Data in R

I would like to simulate, using R, data from the Johnson-Wehrly distribution that is governed by the following pdf: \begin{eqnarray*} f_{X,Y}(x,y) = 2\pi g[2\pi(F_X(x) - F_Y(y))]f_X(x)f_Y(y), \end{...
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Weibull Reliability Test Demonstration

I'll use the following example to help frame my question. The example comes from example 5 in https://www.weibull.com/pubs/2015_RAMS_right_sample_size.pdf Example 5: Let's assume that the failure ...
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Dealing with Tall, Thin, Skewed Data

I'm working with a dataset that shows particle movement. There are three broad cases that I see in my data, when they are negatively skewed, approximately normal, or positively skewed. My end goal is ...
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Intuition behind Weibull distribution?

I don't understand the physical meaning of Weibull distribution's $k$ parameter. Here is a simplified formula of cumulative probability function of Weibull in the simplest form: $$p(\xi \geq x) = e^{-(...
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Inverse 4-parameters Cumulative Weibull Distribution

May someone write the inverse of the FOUR-parameters Weibull cumulative distribution (percent point function), please? I am referring to the 4-parameters formula appearing in Sigmaplot.
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How to simulate survival data with censoring using R

I want to simulate survival data with a sample size of N=100, which follows the Weibull distribution with proportional hazards and constant baseline hazard. Two correlated covariates, which follow ...
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What is the difference between finding the hazard function by using an NHPP and fitting a Weibull curve to the data for a repairable system?

When modelling a repairable system, one should use a non-homogeneous Poisson Process (NHPP). E.g., the moment the hazard function I use in the NHPP is a Weibull function. However, I have difficulty ...
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No observations for specific group - group comparison still possible?

I am conducting a Weibull Survival analysis (recurrent event) with the time-frame between 1970 and 2010. One question is the difference in survival time between gender. However in the earlier years ...
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Most Powerful test for indicating exponential or Weibull distribution [closed]

Let $X_1,...,X_n$ be iid distribution function of $F(x)$. I want to test whether $F$ is exponential or Weibull. This means that either $F(x)=1-exp(-x), x>0$ (exponential) $F(x)=1-exp(-x^{\theta}), ...
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Remaining useful life for Weibull distributed lifetimes

Suppose we model component lifetimes with a two-parameter Weibull distribution. With $\alpha$ as the scale parameter and $\beta$ as the shape parameter, the component's mean survival time is known to ...
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Get Continuous Distribution from Discrete Variable: Problem 6.77 of Wackerly, Mendenhall, Schaeffer, 5th Ed

Problem Statement: $\newcommand{\szdp}[1]{\!\left(#1\right)}$ Let $v$ denote the volume of a three-dimensional figure. Let $Y$ denote the number of particles observed in volume $v,$ and assume that $Y$...
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How to calculate number of cycles in twenty year from a daily distribution

I am asked to determine a distribution of the number of cycles a component is expected to do during its entire lifetime. What is do have now is a distribution of cycles the component makes per day. I ...
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4 votes
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Probability of Weibull RV conditional on another Weibull RV

Let $X, Y$ be independent Weibull distributed random variables and $x>0$ a constant. Is there a closed form solution to calculating the probability $$P(X<x|X<Y)?$$ Or maybe a way to ...
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