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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80 views

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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1answer
283 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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39 views

Likelihood ratio test Weibull distributed r.v -- problem calculating the critical region

Let $X$ be a r.v which is Weibull distributed with $k=4$ and $\lambda>0$. I'm looking at the following test: \begin{align*} H_0:\lambda &= 1\\ H_1: \lambda&\not = 1. \end{align*} I have ...
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1answer
24 views

What is (are) scenerios and practical settings that can possibly lead to the weibull-log-Logistic mixture distribution?

In my paper I studied Weibull-loglogistic mixture distributions in reliability and life testing, some structural properties of the model are presented including moments, reliability, hazard rate ...
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472 views

In comparing the exponential and Weibull distributions, why "rate" for exponential and "scale" for Weibull?

When comparing the exponential CDF with the Weibull CDF, we see: Exponential: ${\displaystyle F(x)=1-e^{-\lambda x}}$ Weibull: ${\displaystyle F(x)=1-e^{-(x/\lambda)^{k}}}$ I understand how the ...
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1answer
255 views

Conditional expectation of a Weibull distributed random variable

Let $X$ be a Weibull Distributed random variable. I want to calculate $E[X\mid X \in [a,b]]$, where $a>0$, $b>0$. Is there a closed form solution for this, and if so, how can I calculate it?
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2answers
221 views

How to draw from conditional Weibull distribution

I would like to draw random numbers in R from a conditional Weibull distribution which is given by P(x<=t+T| x>T) = 1-(1-F(t+T))/(1-F(T)), where ...
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1answer
1k views

Interpretation of Weibull Accelerated Failure Time Model Output

In this case study I have to assume a baseline Weibull distribution, and I'm fitting an Accelerated Failure Time model, which will be interpreted by me later on regarding both hazard ratio and ...
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1answer
187 views

Interval Censored data for WeibullFitter in Lifelines python module [closed]

I am getting different answer using lifelines module for interval censored data fitting using WeibullFitter() function. ...
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0answers
133 views

KL divergence for Generalized Extreme Value distribution

I have found a derivation for the Kullback–Leibler divergence between 2 Gumbel distributions here: http://www.mast.queensu.ca/~communications/Papers/gil-msc11.pdf on page 64 That document also has a ...
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1answer
122 views

Conditional mean of Weibull to the power of N

How can I (is it possible to) derive the conditional expectation of a variable $w$ that follows a 2 parameter Weibull Distribution $W(\lambda,k)$ with $\lambda$ scale parameter and $k$ shape parameter?...
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scipy.stats failing to fit Weibull distribution unless location parameter is constrained

Here is a demo set of data points that are drawn from a larger sample. I fit a Weibull distribution in R using the {fitdistrplus} package, and get back reasonable ...
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175 views

Fisher's information for weibull 2 parameter

I want to find Fisher's information $I(\theta)$ with $-E(\frac{d^2(ln(fx))}{d\theta^2})$ but in two parameters, the expectation is too complex for me. Is there something about the Weibull distribution ...
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0answers
67 views

Why did the log likelihood decrease with additional parameters?

I'm trying to decide the effect of some factors on the time for an event to happen . Specifically, I am looking at how long it takes for the subject to pass a test (recognize the stimulus) when ...
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74 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 ...
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54 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) \...
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1answer
739 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 ...
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0answers
38 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 ...
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1answer
136 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 ...
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1answer
25 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 ...
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1answer
113 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 ...
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0answers
312 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 ...
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0answers
151 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 ...
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0answers
465 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}{\...
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123 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? (...
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1answer
150 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 ...
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0answers
323 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 ...
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0answers
107 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 $b$ ...
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0answers
15 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 ...
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1answer
926 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 ...
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46 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, $...
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2answers
73 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 ...
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2answers
515 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 ...
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1answer
718 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 ...
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1answer
175 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 ...
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1answer
72 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 ...
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1answer
450 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 ...
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0answers
64 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{\...
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186 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 ...
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0answers
338 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 ...
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1answer
150 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 ...
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97 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 ...
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0answers
501 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 ...
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0answers
444 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 ...
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268 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 ...
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1answer
705 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 ...
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0answers
166 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 ...
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1answer
739 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 $f_T(t) = \alpha \lambda (\lambda t)^{\alpha - 1} \exp(-(\lambda t)^\alpha)$. ...
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36 views
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1answer
107 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 ...