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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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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Applications of the Weibull and Reversed Weibull distribution

I'm trying to get some intuition for the GEV distributions. As I understand, the GEV distributions derive from the limiting maximum distributions, one of which is the Type III distribution, also ...
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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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Estimating a non-linear (Weibull) term in linear mixed effects model (nlme)

I'm attempting to fit a mixed effects model to some data with several predictors. However, one of the predictors has a distinctly non-linear relationship with the response variable. After some ...
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1answer
84 views

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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Averaging the parameters of multiple weibull models

I have multiple different weibull models whose parameters have been estimated on different populations. I would like to "average" those different models into one model based on my beliefs of ...
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Finding Weibull parameters based on KM curve provided in a paper

I need to estimate parameters for a weibull (or any other appropriate function) based on Kaplan-Meier curves and confidence intervals found in research papers. See figure 3 in this paper as an example:...
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Aggregating (taking the mean of) a censored variable

This post is related to this post. I have survey data, with a (censored) range from 0-100, that looks as follows: ...
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1answer
166 views

How to interpret coefficients from weibull regression for variables of proportion?

I want to fit a weibull regression model. The variables are however given as proportions (i.e. they are in interval <0,1> ... is this compositional data if they do not sum up to 1?). An example ...
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Rationale for normalization of Weibull distribution?

I am reading a paper which normalizes a Weibull distribution (equation 2): $$ y_{ij} = \frac{ 1 - \exp \left[ - \left( \frac{t_j}{\beta} \right)^\alpha \right] }{ 1 - \exp \left[ - \left( \frac{...
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flexsurvreg - shape and scale proportional hazard model

Please see below codes and plot for fitted curves to Kaplan-Meier data (weibull in this example) using the ovarian data. Based on the estimates, the shape and scale of the fitted Weibull distribution ...
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Building Confidence Intervals From Monte Carlo Simulations

I have a discrete Markov process that I am running Monte Carlo simulations to estimate the distribution parameters, with the ultimate goal of producing a mean-time-to-failure (MTTF) estimate within a ...
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2answers
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Fourth class of extreme-value distributions?

The generalized extreme-value distribution encompasses three classes of distributions: Frechet, which are regularly varying, infinite right limit. Gumbel, which are not regularly varying, infinite ...
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Distributions in the Weibull max-domain of attraction

Can I please have a few examples of distributions that, when block-max sampled for extreme values, are in the max-domain of attraction of the Weibull distribution? I know the Beta distrution is, but ...
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Predict expected survival after n months with survreg weibul

Context is a subscription business with a monthly cost. Goal is to understand expected lifetime of a subscription. I have a weibul model via survreg package: ...
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Report expected value or other measure of centrality from Weibull model?

I went through a tutorial on survival analysis and learned to compute the median from a weibull: ...
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279 views

Is Weibull distribution memoryless?

I googled and it seems not. Only exponential distribution is memoryless. Does anyone have an intuitive explanation why it is not? Thanks
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How to model survival analysis when proportional hazards assumption is not met and stratification and time-varying are not possible?

I am modelling a survival analysis over a rather long follow-up period (10 years). My exposure is time-invariant and clearly violates the proportional hazards assumptions so Cox Proportional Hazards ...
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1answer
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Application of Metropolis Hastings

I am trying to implement the Metropolis Hastings algorithm for Bayesian analysis. In this case, the parameter of interest is the scale parameter for a Weibull distribution. The context is for ...
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Parameters weibull distribution

If anyone can help me with this question i would be very thankfull An article in IEEE Transactions on Dielectrics and Electrical Insulation [“Statistical Analysis of the AC Breakdown Voltages of Ester ...
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Weibull with known shape parameter

I am new to Bayesian robustness. If I have Weibull likelihood $X$~ Weibull($\lambda$, $\beta$)$= \lambda \beta x^{-\beta} \exp(-\lambda x^\beta)$ with $\lambda$ unknown and $\beta$ known. we know that ...
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Why data points on Weibull plot lies outside of probability line?

As shown on the pic from ReliaSoft wiki site below. Data points located not exactly on the probability line. If parameters estimated with MLE, then F(t) for plotting data points and probability line ...
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Find the mode of the Weibull distribution

I am using the matlab curve fitting tool. It allows to use the Weibull distribution, using this formula: $$f(x)=abx^{b-1}\exp(-ax^b). $$ Unfortunately this is not the formula that I found on Wikipedia....
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Random Censoring scheme in Weibull Distribution

I'm trying to derive the estimators of the parameters using maximum likelihood method for Weibull distribution in random censoring scheme $f(t)=\alpha\lambda(\lambda t)^{\alpha -1}e^{{-\lambda t}^{\...
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Simulating Proportional Hazards Weibull model with 2 binary variables, incorrect estimation?

I am simulating survival times from a Weibull(5,3), and I also simulate 2 spurious binary covariates. When I fit a proportional hazards model with Weibull baseline, ...
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1answer
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incomplete gamma function in R (conditional mean of Weibull to the power of N)

I am trying to calculate: $$ E(w^n | \underline{w} < w < \bar{w}) $$ where $w$ follows a 2 parameter Weibull distribution $w \sim W(\lambda,k)$ From a previous question, I know the following ...
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Prove that the MLE exists almost surely and is consistent

I need to show that given an i.i.d sample $X_1,\dots X_n$ arising from the model: $$\{f(x,\theta)=\theta x^{\theta-1}exp\{-x^{\theta}\},x>0,\theta\in (0,\infty)\}$$ that the MLE exists with ...
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How can I write the analytic gradient for my maximum likelihood estimation for Weibull Distribution using Monte Carlo Simulation in R?

I'm using the two parameter Weibull distribution, generating samples and estimating the loglikelihood. The Weibull density function I'm using is this: The Weibull log likelihood I'm using is this one:...
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Generating weibull survival times using the built in rweibull function vs manually defining the hazard (using the gems package in R)

I am trying to generate survival times from a weibull distribution using the gems package, and calculate the shape and scale parameters of that weibull distribution using flexsurvreg The gems package ...
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Unable to calculate the shape and scale parameters of weibull distribution from data simulated through either gems or simsurv in R

I am trying to simulate survival data from a weibull distribution with shape = 1.3 and scale = 1.1. I am then fitting a weibull survival model to the data, to try and calculate back the values of 1.3 ...
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How to find cumulative hazard when we have both start time and event time in r

I have the time at start($x_0$) of the study and failure time/censor time($x_t$) for each patient. I want to calculate the Nelson Aalen estimate for each patient and bind it to the data. First of all, ...
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242 views

Weibull distribution median

I am working with the Weibull model with this pdf: The standard pdf that the some R functions perform is : I am required to find the median, which in the standard parameterisation is $\lambda (\ln2)^{...

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