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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asymptotic unbiasedness of weibull mle

It's known that the MLEs of the two-parameter Weibull distribution scale and shape parameters are not available in a closed form. It is, however, known that they do exist, are unique, and moreover, ...
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5k views

Conjugate of Weibull with shape known

This isn't exactly a homework problem but rather a self-selected problem I'm doing to prepare for a midterm. I can see from Wikipedia that it is an inverse gamma but I am unable to reach the ...
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293 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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2k views

Weibull Distribution v/s Beta Distribution

I've recently fallen in love with the Weibull Distribution and have gotten a reason to see if there's a mapping of this distribution to an interval (0,1). After plotting the Beta Distribution against ...
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79 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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176 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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501 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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346 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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194 views

Confidence bounds for Weibull MTTF

I have three times-to-failure (TTFs) as 28, 40, 43. I fit a Weibull distribution on the data, and want to calculate a 95% confidence interval for the mean-time-to-failure (MTTF). Using ...
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69 views

Weibull regression sensitive to scaling of predictors?

I'm running a Weibull regression and decided to simulate data to assure myself that the model is able to recover the true parameters. ...
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1answer
238 views

Detect the correct distribution from a small sample size by using fitdistrplus in R

The simplest version of the issue that I am looking for help is: How to detect the correct distribution from a small sample size in R by using fitdistrplus A simpler version: I am generating some ...
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863 views

Monte Carlo simulation for fitting distributions (Weibull and log-normal)

I am working on a computer project which needs statistical analysis and I am not much of a statistic person. I have a Bluetooth (BT) detector device which detects passing Bluetooth devices (i.e one ...
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162 views

Likelihood function for a Weibull model

I have an assignment for my course Microeconometrics. Currently I am stuck on the following question You are asked to help out with the statistics of a medical study. We are interested in the time ...
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1k views

Confidence intervals for extreme value distributions

I have wind data that i'm using to perform extreme value analysis (calculate return levels). I'm using R with packages 'evd', 'extRemes' and 'ismev'. I'm fitting GEV, Gumbel and Weibull distributions,...
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275 views

Accelerated Failure Time scale parameter excessively large when data is right censored

I am using an accelerated failure time model with the Weibull distribution to predict failure times. My failure times range from 1 - 365, with many (80%) data points that are right censored (no ...
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69 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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141 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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120 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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66 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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189 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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199 views

Proof of alternative parameterization of Weibull Survival Model

In Parametric Survival Models by German Rodrıguez (hyperlink at bottom), it is stated the Exponential and Weibull models can be parameterized in a linear form (with time parameterized as $\log(T)$). ...
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25 views

How to prove the existence of upper truncated point?

Currently I am working on a data-set seems to have a Weibull distribution. Problem is that not sure if Weibull or Truncated-Weibull is better to use. Any methods or Hypothesis test there to prove if ...
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60 views

Independent variables in truncated Weibull distribution

I am relative new to statistics and currently working on a problem about crash rate analysis. It is appears to be a zero-inflated scenario, then I decide to use the hurdle model. The first part will ...
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302 views

R_How to select hyperprior distribution for Beta distribution parameter in R?

I have 2-mixture weibull distrubution. And this distribution haver the portion parameter θ whose value should lie between (0,1). Therefore, I am assuming the prior distribution of θθ to be a beta ...
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273 views

Probability model for duration, how to write log-likelihood function for Weibull distribution to fit aggreate data

Background: I have a basic to moderate knowledge on probability and statistics. I have familiarity with R programming language and optimization routines. I'm reading an excellent article "Jobs, ...
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393 views

It is possible to do a Multiple Weibull regression?

I have a response variable that I would like to explain with several predictors. The response variable is all positive continuous data. Some of the predictors are discrete while others are continuous. ...
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844 views

Variance-Covariance matrix of Weibull Distribution for right-censored data

The probability distribution function, cumulative distribution function and survival function of Weibull distribution are given by respectively, \begin{equation} f(t;\alpha, \beta)= \dfrac{\beta}{\...
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47 views

Is there any way that this function can be a Weibull distribution?

I am currently working on a fatigue life analysis using an old airworthiness standard, Defence Standard 00-970, which was issued by the UK Minister of Defence for British designed military aircraft. ...
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214 views

Why are these MLE estimates biased?

I estimate the parameters of survival data with censoring which is simulated from Weibull distribution. The mean time to event was set to 10 by choosing the combinations of shape and scale ...
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114 views

Variable effect in Weibull and Cox models

Is it possible to compare effect of variable on the survival time in the Cox model and in the Weibull regression model?
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1k views

Fitting the inverse Weibull distribution to data in R

I am trying to fit the Weibull distribution to a dataset in R. I have a dataset, "loss", as a .csv file, and use fitdistr(loss,"invexp"). I received the message: ...
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2k views

Weibull distributed data for correlation analysis

On visual inspection of P-P plots, my time data appears to fit a Weibull distribution better than a normal distribution. I will use the variable for correlations and as a predictor in regression. In ...
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323 views

Spearman correlation of two Weibull distributions

Is there a way to find the Spearman correlation between two Weibull distributions? I need it as a parameter in a copula function for the joint Weibull distribution. I learned that using the Pearson ...
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54 views

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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1answer
55 views

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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27 views

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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34 views

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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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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1answer
23 views

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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46 views

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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41 views

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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51 views

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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813 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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182 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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76 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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57 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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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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52 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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364 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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529 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 ...