The generalized modified Weibull (GMW) distribution extends the modified Weibull distribution by offering a hazard function with various shapes, including constant, increasing, decreasing, unimodal, and bathtub. This paper aims to estimate the four unknown parameters of the GMW distribution using a Bayesian approach, assuming a lack of prior information represented by noninformative priors such as Jeffreys, Uniform, and Gamma priors. The Bayesian analysis considers both censored data and the presence of covariates. The results of the Bayesian inference are compared with those of the maximum likelihood approach. The Markov Chain Monte Carlo (MCMC) algorithm is employed to compute the Bayesian estimators and construct credible intervals. A simulation study evaluates the performance of these estimators, with comparisons made based on bias, mean square error, and coverage probability. Real data sets are analyzed for illustrative purposes.
AguilarG. A. S.MoalaF. A.CordeiroG. M. (2019). Zero-truncated poisson exponentiated gamma distribution: Application and estimation methods. Journal of Statistical Theory and Practice, 13, 1–20.
2.
AnyiamK. E.EzeriohaE. I.OgbonnaJ. C.DanielsM. E. (2024). New generalized nadarajah haghighi distribution: Characterization and applications. Journal of Modern Applied Statistical Methods, 23, 1–17.
BoxG. E.TiaoG. C. (2011). Bayesian inference in statistical analysis. John Wiley & Sons.
5.
CarrascoJ. M.OrtegaE. M.CordeiroG. M. (2008). A generalized modified Weibull distribution for lifetime modeling. Computational Statistics & Data Analysis, 53(2), 450–462.
6.
CasellaG.GeorgeE. I. (1992). Explaining the gibbs sampler. The American Statistician, 46(3), 167–174.
7.
ChibS.GreenbergE. (1995). Understanding the metropolis-hastings algorithm. The American Statistician, 49(4), 327–335.
8.
CordeiroG. M.AlizadehM.RamiresT. G.OrtegaE. M. (2017). The generalized odd half-Cauchy family of distributions: Properties and applications. Communications in Statistics-Theory and Methods, 46(11), 5685–5705.
9.
GelfandA. E.SmithA. F. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85(410), 398–409.
10.
GelmanA.CarlinJ. B.SternH. S.DunsonD. B.VehtariA.RubinD. B. (2013). Bayesian Data Analysis(3rd ed.). Chapman and Hall/CRC.
11.
GilksW. R.RichardsonS.SpiegelhalterD. J. (Eds.) (1996). Markov chain monte carlo in practice. Chapman and Hall, London.
12.
KhalilA.AhmadiniA. A. H.AliM.MashwaniW. K.AlshqaqS. S.SallehZ. (2021). A novel method for developing efficient probability distributions with applications to engineering and life science data. Journal of Mathematics, 2021(1), 4479270.
13.
LaiC. D.XieM. (2006). Stochastic ageing and dependence for reliability. Springer Science & Business Media.
14.
LaiC. D.XieM.MurthyD. N. P. (2003). A modified weibull distribution. IEEE Transactions on Reliability, 52(1), 33–37.
15.
LeeE. T. (1992). Statistical methods for survival data analysis. John Wiley & Sons, Inc.
16.
MartinezE. Z.AchcarJ. A.JácomeA. A.SantosJ. S. (2013). Mixture and non-mixture cure fraction models based on the generalized modified Weibull distribution with an application to gastric cancer data. Computer Methods and Programs in Biomedicine, 112(3), 343–355.
17.
NaseriP.BaghestaniA. R.MomenyanN.AkbariM. E. (2018). Application of a mixture cure fraction model based on the generalized modified Weibull distribution for analyzing survival of patients with breast cancer. International Journal of Cancer Management, 11(5), 1–8.
18.
NiiyamaC. A.MoalaF. A.OikawaS. M. (2017). Bayesian analysis of generalized modified weibull distribution. Revista Brasileira de Biometria, 34(4), 575–596.
19.
O’HaganA.ForsterJ. J. (2004). Kendall’s advanced theory of statistics, volume 2B: Bayesian inference (Vol. 2). Arnold.
20.
OrtegaE. M. M.CordeiroM. G.CarrascoJ. M. F. (2011). The log-generalized modified weibull regression model. Brazilian Journal of Probability and Statistics, 25(1), 64–89.
21.
PhamH.LaiC. D. (2007). On recent generalizations of the weibull distribution. IEEE Transactions on Reliability, 56, 454–458.
22.
RafiS. M.RaoK. N.AktharS. (2010). Incorporating generalized modified Weibull TEF into software reliability growth model and analysis of optimal release policy. Computer and Information Science, 3(2), 145–162.
23.
RehmanH.ChandraN.EmuraT.PandeyM. (2023). Estimation of the modified Weibull additive hazards regression model under competing risks. Symmetry, 15, 485.
24.
ShamaM. S.AlharthiA. S.AlmulhimF. A., et al. (2023). Modified generalized Weibull distribution: Theory and applications. Scientific Reports, 13, 12828.
25.
SmithA. F. M.RobertsG. O. (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). Journal of the Royal Statistical Society, Series B, 55, 3–24.
26.
WuH.RahmanM.PatwaryM. S. A. (2016). A study of a generalized modified Weibull model: An exponentiated Weibull case. Advances and Applications in Statistics, 49(5), 357–367.
