Weibull Gamma Distribution Research Articles

On the Comparison between the Reliability of Units Produced by Different Production Lines

AbstractThe paper discusses how to evaluate the reliability of units produced by different production lines. The procedure is based on selecting independent random samples of units produced by different production lines and then evaluating reliability functions for each group of units. The comparison between these reliability functions at a given time allows manufacturing experts to evaluate the effectiveness of production lines. A statistical methodology has been taken based on the assumption that the lifetime of units produced by each product line has a Weibull Gamma distribution. Then, real‐world data are used to illustrate the study's contribution to reliability theory applications.

Statistical modelling of the joint probability density function of air density and wind speed for wind resource assessment: A case study from China

This paper proposes a joint probability density function of air density and wind speed, aiming to integrate the air density distribution into statistical wind resource models, thereby helping better understand the correlation between air density and wind speed at different spatiotemporal scales. Hourly air pressure, temperature, and wind speed time series data from 1745 meteorological stations distributed over China for the period 2008–2019 were used to calculate the empirical distributions of air density and wind speed. Four one-component probability density functions and ten two-component mixture probability density functions were fitted to the empirical distributions. It is indicated that the five-parameter Weibull–Gamma distribution is able to achieves more accurate and stable effects in both unimodal and bimodal air density empirical distribution, and the six-parameter Weibull–Burr distribution is the most appropriate distribution for describing wind speed regimes. The parameterised air density and wind speed marginal distributions were linked using five joint copulas. The goodness-of-fit evaluation of the copula models demonstrates that the Gumbel copula most accurately reproduces the bivariate empirical distribution of air density and wind speed. The application of joint distribution has the capability to simplify the evaluation procedures for wind resource assessment while significantly increasing the accuracy of the evaluation results, and also achieve a systematic assessment of available wind resources, considering the temporal patterns of air density. The results of this study will contribute to offering critical information for making better decisions on wind energy projects to realise full development and effective utilisation of wind resources.

Inferences for Weibull-Gamma Distribution in Presence of Partially Accelerated Life Test

Inferences for Weibull-Gamma Distribution in Presence of Partially Accelerated Life Test

The Weibull-Gamma Distribution: Properties and Applications.

A new member of the Weibull-generated (Weibull-G) family of distributions—namely the Weibull-gamma distribution—is proposed. This four-parameter distribution can provide great flexibility in modeling different data distribution shapes. Some special cases of the Weibull-gamma distribution are considered. Several properties of the new distribution are studied. The maximum likelihood method is applied to obtain an estimation of the parameters of the Weibull-gamma distribution. The usefulness of the proposed distribution is examined by means of five applications to real datasets.

Estimations in Step-stress Partially Accelerated Life Tests for the Compound Weibull-Gamma Distribution Under Type-I Censoring

Estimations in Step-stress Partially Accelerated Life Tests for the Compound Weibull-Gamma Distribution Under Type-I Censoring

Inference on the Stress-Strength Model from Weibull Gamma Distribution

Inference on the Stress-Strength Model from Weibull Gamma Distribution

Estimation of parameters of Weibull\u2013Gamma distribution based on progressively censored data

In this paper, the estimation of parameters of a three-parameter Weibull–Gamma distribution based on progressively type-II right censored sample is studied. The maximum likelihood, Bayes, and parametric bootstrap methods are used for estimating the unknown parameters as well as some lifetime parameters reliability function, hazard function and coefficient of variation. Approximate confidence intervals for the unknown parameters as well as reliability function, hazard function and coefficient of variation are constructed based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators (MLEs), and log-transformed MLEs. In addition, two bootstrap CIs are also proposed. Bayes estimates of the unknown parameters and the corresponding credible intervals are obtained by using the Gibbs within Metropolis–Hasting samplers procedure. Furthermore, the results of Bayes method are obtained under both the balanced squared error loss and balanced linear-exponential loss. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, a Monte Carlo simulation study is carried out to investigate the precision of the Bayes estimates with MLEs and two bootstrap estimates, also to compare the performance of different corresponding CIs considered.

Recurrence Relations for Moments of Dual Generalized Order Statistics from Weibull Gamma Distribution and Its Characterizations

In this paper, we establish explicit forms and new recurrence relations satisfied by the single and product moments of dua l generalized order statistics from Weibull gamma distribution (WGD). The results include as particular cases the relations for moments of reversed order statistics and lower records. We present characterizations of WGD based on (i) recurrence relation for single moments, (ii) truncated moments of certain function of the variable and (iii) hazrad function.

Progressively Censored Data from The Weibull Gamma Distribution Moments and Estimation

In this paper, we establish new recurrence relations satisfied by the single and product moments of the progressively type-II right censored order statistics from non truncated and truncated Weibull gamma distribution (WGD), and derive approximate moments of progressively type-II right censored order statistics from this distr ibution. Using these moments to derive the best linear unbiased estimates (BLUE' s) and maximum likelihood estimates (MLE' s) of the location and scale parameters from the Weibull gamma distribution. In addition, we use Monte-Carlo simulation method to obtain the (MSE) of (BLUE' s) and (MLE' s) and make comparison between them. Finally, a numerical examples based on simulation and real data to illustrate the inference procedures developed in this distribution are presented.

Progressively Censored Data from The Weibull Gamma Distribution Moments and Estimation

Progressively Censored Data from The Weibull Gamma Distribution Moments and Estimation