Estimation in Generalized Lindley distribution with randomly censored data
DOI:
https://doi.org/10.19139/soic-2310-5070-1183Keywords:
Generalized Lindley distribution, Random censoring, maximum likelihood estimation, Bayes estimation, MCMC method, HPD credible intervalAbstract
In this article, we obtained the point and interval estimations for a generalized Lindley distribution (GLD) based on randomly censored data. The maximum likelihood (ML) and Bayes estimation method are used to estimate the unknown parameters of the GLD. Furthermore, approximate confidence intervals (ACIs) for the unknown parameters were constructed. Markov chain Monte Carlo (MCMC) method applied to find the Bayes estimation. Also, highest posterior density (HPD) credible intervals (CRIs) were obtained for the parameters. Gibbs within Metropolis-Hasting samplers used to generate samples from the posterior density functions. A real data set is discussed to illustrate the proposed methods. we performed a Monte Carlo simulation study.References
Akaike H., (1974) A new look at the statistical models
identification. \emph{IEEE Transactions on Automatic Control}, 19,
716-723.
Ali S., Aslam M., \& Kazmi S.M.A, (2013) A study of the effect of
the loss function on Bayes estimate, posterior risk and hazard
function for Lindley distribution. \emph{Applied Mathematical
Modelling} 37, 6068–6078.
Balakrishnan N. \& Aggarwala R., (2000). Progressive Censoring:
Theory, Methods and Applications. \emph{Springer Science and
Business Media}, New York.
Chaturvedi A., Kumar N., \& Kumar K., (2018). Statistical
inference for the reliability functions of a family of lifetime
distributions based on progressive Type II right censoring.
\emph{Statistica}, \emph{78}(1), 81–101.
Chen M., H., \& Shao Q. M., (1999). Monte Carlo estimation of
Bayesian credible and HPD intervals. \emph{Journal of
Computational and Graphical Statistics}, \emph{8}(1), 69–92.
Danish M. Y., \& Aslam M., (2013) Bayesian estimation for randomly
censored generalized exponential distribution under asymmetric
loss functions. \emph{Journal of Applied Statistics}, 40,
1106-1119.
Danish M. Y., \& Aslam M., (2014) Bayesian inference for the
randomly censored Weibull distribution. \emph{Journal of
Statistical Computation and Simulation}, 84, 215-230.
Danish M. Y., Arshad I. A., \& Aslam M., (2018) Bayesian
inference for the randomly censored Burr-type XII distribution.
\emph{Journal of Applied Statistics}, 45, 270-283.
Dube M., Garg R., \& Krishna H., (2016) On progressively first
failure censored Lindley distribution. \emph{Computational
Statistics},
31, 139–163.
Efron B., \& Tibshirani R. J., (1994) An Introduction to the
Bootstrap. \emph{Chapman and Hall/CRC}, New York.
Efron B., (1982) The Jacknife, the bootstrap and other resampling
plans. \emph{CBMS-NSF Regional Conference Series in Applied
Mathematics Society}, SIAM 38.
EL-Sagheer R. M., Mohamed A. W. Mahmoud, \& Hasaballah M.
Hasaballah. (2020) Bayesian Inference for the Randomly Censored
Three-Parameter Burr XII Distribution. \emph{Applied Mathematics
and Information Sciences}, \emph{14} (2), 1-11.
Garg R., Dube M., Kumar K., \& Krishna H., (2016) On randomly
censored generalized inverted exponential distribution.
\emph{American Journal of Mathematical and Management Sciences},
35, 361-379.
Garg R., Dube M., \& Krishna H., (2020) Estimation of Parameters
and Reliability Characteristics in Lindley Distribution Using
Randomly Censored Data. \emph{STATISTICS, OPTIMIZATION AND
INFORMATION COMPUTING}, 8, 80–97.
Ghitany, M.E., Atieh, B. \& Nadarajah, S. (2008). Lindley
distribution and its application, \emph{ Mathematics and Computers
in Simulation}, 78, 493-506.
Gilbert J. P., (1962) Random Censorship. \emph{ Ph.D. thesis,
University of Chicago.}
Hall P., (1988) Theoretical comparison of bootstrap confidence
intervals. \emph{The Annals of Statistics}, 16, 927-953.
Kim J. H., (1993) Chi-square goodness-of-fit tests for randomly
censored data. \emph{The Annals of Statistics}, 21, 1621-1639.
Kumar K., Krishna H., \& Garg R., (2015) Estimation of P(Y < X) in
Lindley distribution using progressively first failure censoring.
\emph{International Journal of System Assurance Engineering and
Management}, 6, 330-341.
Kumar K., Garg R., \& Krishna H., (2017). Nakagami distribution as
a reliability model under progressive censoring.
\emph{International Journal of System Assurance Engineering and
Management}, \emph{8}(1), 109–122.
Krishna H., \& Kumar K., (2011) Reliability estimation in Lindley
distribution with progressively type II right censored sample.
\emph{Mathematics and Computers in Simulation}, 82, 281-294,
Krishna H., Vivekanand \& Kumar K.,(2015) Estimation in Maxwell
distribution with randomly censored data. \emph{Journal of
Statistical Computation and Simulation}, 85, 3560- 3578.
Krishna H., \& Goel N., (2017) maximum likelihood and Bayes
estimation in randomly censored geometric distribution.
\emph{Journal of Probability and Statistics}, 3, 1-12.
Krishna H., \& Goel N., (2018) Classical and Bayesian inference
in two parameter exponential distribution with randomly censored
data. \emph{Computational Statistics}, 33, 249-275.
Lindley, D.V. (1958). Fiducial distributions and Bayesian theorem.
\emph{ Journal of the Royal Statistical Society B}, 20, 102-107.
Mazucheli J., \& Achcar J. A., (2011) The Lindley distribution
applied to competing risks lifetime data. \emph{Computer Methods
and Programs in Biomedicine}, 104, 188-192.
Nadarajah, S., Bakouch, H. S., \& Tahmasbi, R. (2011). A
generalized Lindley distribution. \emph{Sankhya B}, 73, 331-359.
ROBERT, G. CASELLA (2004). Monte Carlo Statistical Methods.
\emph{Springer Science and Business Media, New York}.
Schwarz G., (1978) Estimating the dimension of a model. \emph{The
Annals of Statistics}, 6, 421-464.
Zheng G., \& Gastwirth J. L., (2001) On the Fisher information in
randomly censored data. \emph{Statistics and Probability Letters},
52, 421-426.
identification. \emph{IEEE Transactions on Automatic Control}, 19,
716-723.
Ali S., Aslam M., \& Kazmi S.M.A, (2013) A study of the effect of
the loss function on Bayes estimate, posterior risk and hazard
function for Lindley distribution. \emph{Applied Mathematical
Modelling} 37, 6068–6078.
Balakrishnan N. \& Aggarwala R., (2000). Progressive Censoring:
Theory, Methods and Applications. \emph{Springer Science and
Business Media}, New York.
Chaturvedi A., Kumar N., \& Kumar K., (2018). Statistical
inference for the reliability functions of a family of lifetime
distributions based on progressive Type II right censoring.
\emph{Statistica}, \emph{78}(1), 81–101.
Chen M., H., \& Shao Q. M., (1999). Monte Carlo estimation of
Bayesian credible and HPD intervals. \emph{Journal of
Computational and Graphical Statistics}, \emph{8}(1), 69–92.
Danish M. Y., \& Aslam M., (2013) Bayesian estimation for randomly
censored generalized exponential distribution under asymmetric
loss functions. \emph{Journal of Applied Statistics}, 40,
1106-1119.
Danish M. Y., \& Aslam M., (2014) Bayesian inference for the
randomly censored Weibull distribution. \emph{Journal of
Statistical Computation and Simulation}, 84, 215-230.
Danish M. Y., Arshad I. A., \& Aslam M., (2018) Bayesian
inference for the randomly censored Burr-type XII distribution.
\emph{Journal of Applied Statistics}, 45, 270-283.
Dube M., Garg R., \& Krishna H., (2016) On progressively first
failure censored Lindley distribution. \emph{Computational
Statistics},
31, 139–163.
Efron B., \& Tibshirani R. J., (1994) An Introduction to the
Bootstrap. \emph{Chapman and Hall/CRC}, New York.
Efron B., (1982) The Jacknife, the bootstrap and other resampling
plans. \emph{CBMS-NSF Regional Conference Series in Applied
Mathematics Society}, SIAM 38.
EL-Sagheer R. M., Mohamed A. W. Mahmoud, \& Hasaballah M.
Hasaballah. (2020) Bayesian Inference for the Randomly Censored
Three-Parameter Burr XII Distribution. \emph{Applied Mathematics
and Information Sciences}, \emph{14} (2), 1-11.
Garg R., Dube M., Kumar K., \& Krishna H., (2016) On randomly
censored generalized inverted exponential distribution.
\emph{American Journal of Mathematical and Management Sciences},
35, 361-379.
Garg R., Dube M., \& Krishna H., (2020) Estimation of Parameters
and Reliability Characteristics in Lindley Distribution Using
Randomly Censored Data. \emph{STATISTICS, OPTIMIZATION AND
INFORMATION COMPUTING}, 8, 80–97.
Ghitany, M.E., Atieh, B. \& Nadarajah, S. (2008). Lindley
distribution and its application, \emph{ Mathematics and Computers
in Simulation}, 78, 493-506.
Gilbert J. P., (1962) Random Censorship. \emph{ Ph.D. thesis,
University of Chicago.}
Hall P., (1988) Theoretical comparison of bootstrap confidence
intervals. \emph{The Annals of Statistics}, 16, 927-953.
Kim J. H., (1993) Chi-square goodness-of-fit tests for randomly
censored data. \emph{The Annals of Statistics}, 21, 1621-1639.
Kumar K., Krishna H., \& Garg R., (2015) Estimation of P(Y < X) in
Lindley distribution using progressively first failure censoring.
\emph{International Journal of System Assurance Engineering and
Management}, 6, 330-341.
Kumar K., Garg R., \& Krishna H., (2017). Nakagami distribution as
a reliability model under progressive censoring.
\emph{International Journal of System Assurance Engineering and
Management}, \emph{8}(1), 109–122.
Krishna H., \& Kumar K., (2011) Reliability estimation in Lindley
distribution with progressively type II right censored sample.
\emph{Mathematics and Computers in Simulation}, 82, 281-294,
Krishna H., Vivekanand \& Kumar K.,(2015) Estimation in Maxwell
distribution with randomly censored data. \emph{Journal of
Statistical Computation and Simulation}, 85, 3560- 3578.
Krishna H., \& Goel N., (2017) maximum likelihood and Bayes
estimation in randomly censored geometric distribution.
\emph{Journal of Probability and Statistics}, 3, 1-12.
Krishna H., \& Goel N., (2018) Classical and Bayesian inference
in two parameter exponential distribution with randomly censored
data. \emph{Computational Statistics}, 33, 249-275.
Lindley, D.V. (1958). Fiducial distributions and Bayesian theorem.
\emph{ Journal of the Royal Statistical Society B}, 20, 102-107.
Mazucheli J., \& Achcar J. A., (2011) The Lindley distribution
applied to competing risks lifetime data. \emph{Computer Methods
and Programs in Biomedicine}, 104, 188-192.
Nadarajah, S., Bakouch, H. S., \& Tahmasbi, R. (2011). A
generalized Lindley distribution. \emph{Sankhya B}, 73, 331-359.
ROBERT, G. CASELLA (2004). Monte Carlo Statistical Methods.
\emph{Springer Science and Business Media, New York}.
Schwarz G., (1978) Estimating the dimension of a model. \emph{The
Annals of Statistics}, 6, 421-464.
Zheng G., \& Gastwirth J. L., (2001) On the Fisher information in
randomly censored data. \emph{Statistics and Probability Letters},
52, 421-426.
Downloads
Published
2026-06-08
How to Cite
Marganpoor, S., & Ranjbar, V. (2026). Estimation in Generalized Lindley distribution with randomly censored data. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-1183
Issue
Section
Research Articles
License
Copyright (c) 2026 Shahdie Marganpoor, Vahid Ranjbar
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
