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.

Filter by
Sorted by
Tagged with
3
votes
0answers
32 views

What methods are there for estimating distributions based on histograms?

I recently worked on a consulting project where a client wanted to estimate gamma and weibull distributions based purely on histograms rather than raw-data. I have never worked with problems like that ...
1
vote
0answers
47 views

Finding Quantiles and Sampling from a Mixture of Distributions

I am trying to replicate a result in this paper, specifically I am trying to implement the mixture distribution on page 9 of the document. The authors describe a hazard function: $$ h(x):=h_{1}(x) \...
0
votes
0answers
23 views

How to calculate time to failure from parameters in Weibull simulation package? [closed]

I am doing some simulations with R and I am using the package simsurv to get random event times based on a Weibull distribution, ...
1
vote
1answer
52 views

How to fit Weibull distribution using “MME” method and find the estimates in R [closed]

I am trying to fit a Weibull distribution using Moments Matching Estimation (MME) method. Specifically I am trying to estimate the shape parameter $k$ and the scale $\lambda$. I am currently using R ...
1
vote
0answers
23 views

Hazard rate from Weibull vs. cumulative hazard plot does not match

) My problem is that I have HR for a factor named "Selvrisiko" and I get the output estimates (HR) (Upper bound) (Lower bound) as: but when I plot (Kaplan - Meier) cumulative hazard for the ...
3
votes
1answer
69 views

Intersection point of two Weibull PDFs

I am wondering if there is an algebraic solution (i.e. an equation) to find the intersection point(s) of two Weibull probability densities that have different scale and shape parameters. While I have ...
0
votes
0answers
17 views

More efficient way to calculate convolution of Weibull distribution

Hi I was trying to compute the convolution of Weibull distribution as follows with parameter t, lambda(scale parameter) and k: ...
0
votes
1answer
17 views

Is it true that for the Weibull distribution a value of $k$ for $ k > 1 $ indicates that the failure rate increases with time?

When describing the Weibull distribution on Wikipedia, it is claimed, among other things, that "A value of $ k > 1 $ indicates that the failure rate increases with time." However, for $ k > 3 ...
0
votes
0answers
11 views

What happens when shape parameter of Weibull distribution goes to 0

When shape parameter of Weibull goes to infinity, it converges to a Dirac delta distribution. I wonder what happens when Weibull shape parameter goes to 0?
0
votes
0answers
24 views

Parametric shared frailty models with individual monotone yet population non-monotone hazard

I'm fitting parametric survival models with/without shared frailty on individuals. The hazard in my data is very low at first, then increases and finally decreases again, sort of a bell shaped curve. ...
0
votes
0answers
36 views

Predicting hazard in an AFT Weibull model

I have fitted a Weibull Accelerated Failure Time model and my question is how to obtain the hazard. For example in Stata, after fitting a model with streg, typing predict newvar, hazard obtains the ...
0
votes
0answers
17 views

Extended regular variation

In extreme-value theory, an important property of distributions in the Frechet/power-law domain of attraction distribution is "regular variation". My question: What is the corresponding property (if ...
0
votes
1answer
36 views

Can I replace the distribution in Gaussian Process Regression with a different regression?

Sorry for the confusing title. Let me try to clarify: I have a time series of wind speeds with some missing points here and there. I want to interpolate these points and have tried mainly polynomial ...
1
vote
0answers
91 views

Weibull probability Plot? [closed]

I am trying to reproduce a plot from a paper. The plot is a Weibull probability plot and is used to illustrate why a Weibull distribution is appropriate for modelling failure times. The plot is ...
3
votes
0answers
79 views

How are the Rayleigh Distribution and Weibull Distribution related?

I am trying to work out a physically intuitive way of understanding how the Weibull arises. Also according to the Wikipedia entry on the Weibull distribution, there is some how a relation to the ...
2
votes
0answers
78 views

Posterior distribution for Weibull scale parameter with censored data

I am modeling a survival problem using a Weibull distribution with known shape parameter $k$ and unknown scale parameter $\theta$. The PDF and CDF are given by, \begin{align} f(t|k,\theta)=\frac{k}{\...
1
vote
0answers
40 views

Testing for Constant Hazard Function

My colleagues and I have some unemployment data, and we'd like to test the hypothesis that it's drawn from a memoryless distribution (= constant hazard function). Is there a standard test for this? (...
2
votes
1answer
113 views

Why should there be two solutions for each parameter of likelihood ratio equation for Weibull-distribution?

I try to calculate the confidence ínterval of a Weibull distribution by means of the Likelihood method as described in ReliaWiki. In order to find the confidence intervals, I have to solve the ...
3
votes
0answers
98 views

Convergence rate of the maximum of Weibull random variables to a Gumbel distribution

Given a sequence of iid samples $X_1, \dots, X_n,$ where each $X_i$ comes from a Weibull distribution with shape parameter $k$ and scale parameter $\lambda$. Then it is a well-known result that the ...
0
votes
0answers
29 views

survival model with weibull sojourn time in R

I aims to develop multi state survival model in R with the transition time between any two states follows Weibull distribution. However, based on the documentation and as shown in the picture below, I ...
1
vote
0answers
63 views

Weibull distribution fit

I have a random variable $X$ for which it is known a priori that $P(X > x) = \exp(-ax^b)$, i.e. the CDF is given by $F_X(x) = 1-\exp(-ax^b)$. I would like to determine the values of $a$ and $b$ ...
0
votes
0answers
12 views

What data to include in Weibull fit

I have a set of inspection data that I want to fit to a weibull distribution to understand whether further inspection would provide much value. For example, I have 2000 items of which we have ...
0
votes
1answer
154 views

A goodness of fit test for the Weibull distribution

I have data which I have to test to see if it comes from the Weibull distribution. I don't know the parameters so I am looking for a goodness of fit test (like the Lillefors test), preferably which I ...
0
votes
0answers
55 views

Weibull Model in Stata vs R

I am currently trying to replicate a study on war duration, which used Stata's streg function to estimate a parametric Weibull model. The stata code reads: ...
1
vote
0answers
31 views

Predicting survival probability at a future time for proportional hazard model

I have a Weibull proportional hazard model with fitted parameters $\lambda$ and $k$ and a time dependent covariate $x(t)$ with fitted coefficient $\beta$, such that the hazard function is given by, $...
2
votes
2answers
49 views

Weibull Stats for Testing Significance of Ultimate Strength in Mechanical Failure

First, I'll start with some background that may explain the ignorance that will likely be encountered in the remainder of the post. I am an archaeologist attempting to study the flexural strength of ...
0
votes
1answer
55 views

Estimating two-component mixture of Weibull distributions?

Is there any existing package (preferably in Python or Matlab) to estimate the parameters of a two-component Weibull mixture model? And failing that, I am hoping to get some pointers towards rolling ...
0
votes
0answers
26 views

Weibull Distribution with priors on shape and scale diverges

I have a variable that is Weibull Distributed Duration ~ dweib(Shape,Scale) The Shape and Scale parameters are distributed to log-normal and Weibull ...
0
votes
1answer
326 views

Prediction of regression coefficients with XGBoost

I am doing survival analysis. There is a dataset of items (id, group_id, observed lifetime, censorship status), each item belongs to a certain group. Each item is ...
0
votes
1answer
79 views

Validity of Weibull distribution [closed]

I have come across validation engineers picking the Weibull distribution as a way to generate test stimulus. When they do this, they seem to chose the parameterisation without reference to any ...
0
votes
1answer
30 views

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 ...
0
votes
0answers
53 views

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 ...
3
votes
1answer
131 views

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 ...
2
votes
0answers
26 views

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{\...
0
votes
0answers
83 views

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 ...
1
vote
0answers
62 views

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 ...
4
votes
1answer
104 views

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 ...
0
votes
0answers
60 views

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 ...
1
vote
0answers
199 views

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 ...
1
vote
0answers
176 views

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 ...
3
votes
0answers
78 views

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 ...
0
votes
1answer
326 views

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 ...
2
votes
0answers
68 views

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 ...
0
votes
1answer
321 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 $f_T(t) = \alpha \lambda (\lambda t)^{\alpha - 1} \exp(-(\lambda t)^\alpha)$. ...
0
votes
0answers
35 views
1
vote
1answer
81 views

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 ...
0
votes
1answer
59 views

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) ...
2
votes
1answer
824 views

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 $\lambda,k > 0$...
1
vote
0answers
192 views

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´...
0
votes
1answer
51 views

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 ...