Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

0
votes
0answers
5 views

What's a simple explanation for risk and its formula in survival analysis, weibull regression

I have that if the model is $\ln(\mu_i) = \beta_0 + \beta_1 x_1$ where $x_1 \in \{0,1\}$ and represents tired (or anything suitable, sex, etc). The model also has a shape parameter, $\gamma$. ...
0
votes
1answer
28 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
17 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
24 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
15 views

How do I estimate parameters of Weibull distribution in R based on a given dataset? [duplicate]

Here I got the Weibull distribution function like this, and how can I estimate the parameters by the below data set?
0
votes
0answers
32 views
1
vote
1answer
19 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
31 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) ...
0
votes
0answers
26 views
1
vote
1answer
27 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
35 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
0answers
4 views

Duration Analysis with Clumping at Infinity?

I am currently trying to build a model to analyze how price setting today affects how long it takes for a customer to return. My first cut was to fit a Weibull regression where the log of the scale ...
0
votes
1answer
25 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 ...
0
votes
0answers
75 views

What is the Most Probable Maximum for a Weibull distribution?

The title says most of it. I have a signal from which I need to calculate the most probable maximum extreme value. The approaches I have so far are: 1- Assuming a Gaussian process, fit a Rayleigh ...
0
votes
0answers
29 views
0
votes
0answers
20 views

How can we predict reliability for type 1 censored data?

I am working on a somewhat challenging problem. I have data for a large set of equipment. My main research question is: How many units will fail in each future month in the coming decade? So far I ...
2
votes
0answers
37 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 $\log(T)$). ...
0
votes
1answer
86 views

Hazard function for a growing population

I want to model the expected failure rate in a growing population. Each individual has a high infant mortality (e.g. Weibull(shape=0.5, scale=100)). So the ...
0
votes
1answer
11 views

Sensitivity of Weibull survival model to early missing data

I have a few datasets of survival times that appears to be very well-modelled by Weibull distributions; I am mostly interested in whether $k$ is above, below or around 1. However, there is a real ...
2
votes
1answer
64 views

fitting weibull distribution to “wind speed” data

I am trying to fit a weibull distribution to my wind speed data with the following code: fitdistr(av_ws, densfun = "weibull") #av_ws is the wind speed data The ...
3
votes
0answers
32 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 ...
0
votes
0answers
23 views

Cumulative Incidence Plots - Weibull Model - Time Dependent Covariates

I am seeking to create a Cumulative Incidence Plot for a Weibull model with baseline and time-varying covariates. I am using SAS PROC LIFEREG to for this model but there are two issues-one of which is ...
1
vote
0answers
49 views

Moment generating function of a Weibull distribution and root finding heavy and light tailed case

I consider the equation $M_x(v)=1+(1+\beta)\mu$ and I need to find the solution $v>0$ such that the equation is fulfilled. For this example I consider the moment generating function $M_X(v)$ of a ...
1
vote
0answers
80 views

Weibull distribution is not a glm, why?

It is a generalized linear model with a linear combination of covariates related to the response via a canonical link function. Why weibull distribution is not a glm?
4
votes
0answers
173 views

Fisher information matrix in logistic regression

I am self-studying the basics of logistic regression. I came across this sentence: In logistic regression expected and observed information matrixes are equal I am aware that the information ...
2
votes
0answers
17 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 ...
2
votes
0answers
25 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 ...
1
vote
2answers
47 views

Attempting to find mean of Weibull function in R

I am using a Weibull distribution in R, and know that: E(X) = 1000 and Var(X) = 500,000 Knowing: E(X^r) = ($\Gamma$(1+ (r/$\gamma$))) * 1/c^(r/$\gamma$)) I ...
2
votes
1answer
75 views

Why don't I see my points on cullen and frey graph

I have a set of data of 5 members. based on some previous questions , I was expecting to see where my actual points are located on the graph. in my case I see the theoretical but not my points. just ...
3
votes
2answers
167 views

Getting weirdly small cdf and pdf values for a set of data of 5 members in R

I am doing a Weibull and normal distribution analysis for a set of my data which are : 336256 620316 958846 1007830 1080401 So to avoid putting the whole code here, I refer you directly to the ...
0
votes
1answer
39 views

Why is Hazard Function called rate of failure?

I am confused why Hazard Function is called rate of failure. Here is what I understood about Hazard Function. Suppose we are dealing with Weibull and let $f(X)$ be the pdf, $F(X)$ be the cdf. Now, I ...
4
votes
1answer
61 views

Distribution of maximum over minimum of Weibull(alpha, 1)

Let the PDF of Weibull $(\alpha, 1)$ be $$ f_X (x) = \alpha x^{\alpha-1} \exp\left( - x^{\alpha}\right) $$ I know from probability integral transfrom that $$ X_{(1)}^{\alpha} \overset{d}{=} Z_{(1)...
6
votes
1answer
100 views

$\mathbb{E}(\log(X_{max}/X_{min}) )$ of Weibull(alpha, 1)

I'm trying to find the expectation of log(max/min) from n samples of Weibull(alpha, 1). But I keep failing. Can anybody give some hints? I tried: $\mathbb{E}(\log(X_{max}/X_{min}) ) = \int_0^{\...
0
votes
0answers
48 views

Why are Weibull Results Different in R than in Stata?

I'm working with a time-series dataset that looks like the following: I want to run a survival model with a weibull parametrization, but I'm getting different results in Stata and in R. In Stata, ...
0
votes
0answers
46 views

fitting distribution to values (some of which are negative)

I'd like to fit a distribution. ...
3
votes
0answers
33 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. ...
6
votes
1answer
101 views

Marginal density of $X_1$ given that $X_1 + X_2 = d$ where $X_1$ and $X_2$ are iid Weibull?

In their tutorial (page 23) on heavy-tailed distributions, Nair et al. present the following graph (taken from a pre-publication chapter from a book by the same authors): Pictured are the marginal ...
1
vote
1answer
86 views

How to calculate mortality rate or probability of death at time t for various parametric distributions, e.g. Weibull, exponential, log-normal

If I have lambda and gamma, can I estimate that the probability of death at time t, based on a Weibull distribution is: What are similar formulas for the exponential, Gompertz, log-normal, log-...
3
votes
2answers
377 views

Why isn't Weibull Maximum Likelihood Estimation possible with x=0?

As everybody knows, the pdf of the Weibull distribution is defined by $ f(x)= \left(\dfrac{a}{b}\right)\left(\dfrac{x}{b}\right)^{a-1}exp\left(-\left(\dfrac{x}{b}\right)^a\right)\quad \text{for } x \...
2
votes
1answer
127 views

Compare shape and scale parameters between Weibull distributions

I have a number of data sets each containing the measurement of all trees diameter within one hectare. A Weibull function distribution is fitted to the data and for each data set I obtain the ...
1
vote
1answer
45 views

Anyone seen this parametrization of Weibull?

My lecturer uses a parametrization of Weibull that I can't find any where else so I'm wondering are they mistaken. Can anyone confirm if this is legitimate pdf of a Weibull? $$\lambda\theta y^{\...
2
votes
1answer
743 views

Fitting Weibull distribution in R

My sample data: ...
1
vote
0answers
57 views

Estimation of a Weibull distribution. Overview of the methods

I'm looking for a method to estimate the parameters of a Weibull distribution from a given set of data. I know there are several method in literature, but I couldn't understand very well the ...
1
vote
0answers
37 views

Testing Parameter Restrictions in R

I've got duration data that I'm analyzing in R. The exponential and weibull distributions are both commonly used when constructing Accelerated Failure Time models for duration analysis/survival ...
0
votes
0answers
21 views

Weibull hazard Rate for Machine Vibration data

I have vibration measurements of machines over different duration till the Machine breaks down. I have several such records. How do I fit a Weibull model and compute the hazard rate. Is it that for ...
0
votes
0answers
62 views

how to model hourly wind speed data

I am trying to forecast hourly wind speed (HWS) data in Trinidad and Tobago and I have read in the literature that "Direct application of stochastic models (ARMA & ARIMA models) to HWS series is ...
0
votes
0answers
68 views

How to model wind speed with a weibull distribution when there is excessive zeros in the distribution? [duplicate]

Hey I have a data set that contains hourly wind speed for about seven years. I am trying to model the data using a weibull distribution which according to literature is a good fit for hourly wind ...
0
votes
0answers
23 views

fitting boxcox transformation to hourly wind speed

Hey, I am trying to transform and standardize my hourly wind speed dataset to make it make it gaussian shaped. I am doing this to observe the seasonal/periodic variations within my dataset. However ...
1
vote
0answers
47 views

Has the Weibull distribution got pseudovariance?

I have a scholar question about the Weibull distribution, which can be parameterised, among other options, like follow: $f(t)= \lambda \alpha t^{\alpha-1}{exp} \left \{ \lambda t^\alpha \right \}$ ...
1
vote
1answer
93 views

Non-normal distributions vs data transformation

How would an individual decide on treating Non-normal data for, e.g. control charts; data transformation vs Non-normal distributions such as Weibull? I have access to Minitab but the decision point ...