IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i1p677-686.html
   My bibliography  Save this article

The Poisson-exponential lifetime distribution

Author

Listed:
  • Cancho, Vicente G.
  • Louzada-Neto, Franscisco
  • Barriga, Gladys D.C.

Abstract

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set.

Suggested Citation

  • Cancho, Vicente G. & Louzada-Neto, Franscisco & Barriga, Gladys D.C., 2011. "The Poisson-exponential lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 677-686, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:677-686
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00255-0
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. B. Reiser & I. Guttman & Dennis K. J. Lin & Frank M. Guess & John S. Usher, 1995. "Bayesian Inference for Masked System Lifetime Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(1), pages 79-90, March.
    2. Kaifeng Lu & Anastasios A. Tsiatis, 2001. "Multiple Imputation Methods for Estimating Regression Coefficients in the Competing Risks Model with Missing Cause of Failure," Biometrics, The International Biometric Society, vol. 57(4), pages 1191-1197, December.
    3. Karlis, Dimitris, 2009. "A note on the exponential Poisson distribution: A nested EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 894-899, February.
    4. Barreto-Souza, Wagner & Cribari-Neto, Francisco, 2009. "A generalization of the exponential-Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2493-2500, December.
    5. Kus, Coskun, 2007. "A new lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4497-4509, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ausaina Niyomdecha & Patchanok Srisuradetchai, 2023. "Complementary Gamma Zero-Truncated Poisson Distribution and Its Application," Mathematics, MDPI, vol. 11(11), pages 1-13, June.
    2. Rasool Roozegar & Saralees Nadarajah & Eisa Mahmoudi, 2022. "The Power Series Exponential Power Series Distributions with Applications to Failure Data Sets," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 44-78, May.
    3. Hanukov, Gabi, 2022. "Improving efficiency of service systems by performing a part of the service without the customer's presence," European Journal of Operational Research, Elsevier, vol. 302(2), pages 606-620.
    4. Bao Yiqi & Cibele Maria Russo & Vicente G. Cancho & Francisco Louzada, 2016. "Influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(6), pages 1027-1060, May.
    5. Feyza Günay & Mehmet Yilmaz, 2018. "Different Parameter Estimation Methods for Exponential Geometric Distribution and Its Applications in Lifetime Data Analysis," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 8(2), pages 36-43, September.
    6. Gupta, Ramesh C. & Ghitany, M.E. & Al-Mutairi, D.K., 2012. "Estimation of reliability in a parallel system with random sample size," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 83(C), pages 44-55.
    7. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2019. "Performance improvement of a service system via stocking perishable preliminary services," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1000-1011.
    8. Mahmoudi, Eisa & Sepahdar, Afsaneh, 2013. "Exponentiated Weibull–Poisson distribution: Model, properties and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 76-97.
    9. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.
    10. Francisco Louzada & M�rcia A.C. Macera & Vicente G. Cancho, 2015. "The Poisson-exponential model for recurrent event data: an application to bowel motility data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(11), pages 2353-2366, November.
    11. Liu, Xiangwei & He, Daijie & Lodewijks, Gabriel & Pang, Yusong & Mei, Jie, 2019. "Integrated decision making for predictive maintenance of belt conveyor systems," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 347-351.
    12. Silva, Rodrigo B. & Bourguignon, Marcelo & Dias, Cícero R.B. & Cordeiro, Gauss M., 2013. "The compound class of extended Weibull power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 352-367.
    13. Liu, Junfeng & Wang, Yi, 2013. "On Crevecoeur’s bathtub-shaped failure rate model," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 645-660.
    14. Giovani Carrara Rodrigues & Francisco Louzada & Pedro Luiz Ramos, 2018. "Poisson–exponential distribution: different methods of estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 128-144, January.
    15. Manoj Kumar & Sanjay Kumar Singh & Umesh Singh, 2018. "Bayesian inference for Poisson-inverse exponential distribution under progressive type-II censoring with binomial removal," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(6), pages 1235-1249, December.
    16. Bakouch, Hassan S. & Ristić, Miroslav M. & Asgharzadeh, A. & Esmaily, L. & Al-Zahrani, Bander M., 2012. "An exponentiated exponential binomial distribution with application," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1067-1081.
    17. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2020. "A service system with perishable products where customers are either fastidious or strategic," International Journal of Production Economics, Elsevier, vol. 228(C).
    18. Mahmoudi, Eisa & Jafari, Ali Akbar, 2012. "Generalized exponential–power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4047-4066.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Louzada, Francisco & Roman, Mari & Cancho, Vicente G., 2011. "The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2516-2524, August.
    2. Bakouch, Hassan S. & Ristić, Miroslav M. & Asgharzadeh, A. & Esmaily, L. & Al-Zahrani, Bander M., 2012. "An exponentiated exponential binomial distribution with application," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1067-1081.
    3. Manoj Kumar & Sanjay Kumar Singh & Umesh Singh, 2018. "Bayesian inference for Poisson-inverse exponential distribution under progressive type-II censoring with binomial removal," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(6), pages 1235-1249, December.
    4. Rasool Roozegar & Saralees Nadarajah & Eisa Mahmoudi, 2022. "The Power Series Exponential Power Series Distributions with Applications to Failure Data Sets," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 44-78, May.
    5. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.
    6. Silva, Rodrigo B. & Bourguignon, Marcelo & Dias, Cícero R.B. & Cordeiro, Gauss M., 2013. "The compound class of extended Weibull power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 352-367.
    7. Feyza Günay & Mehmet Yilmaz, 2018. "Different Parameter Estimation Methods for Exponential Geometric Distribution and Its Applications in Lifetime Data Analysis," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 8(2), pages 36-43, September.
    8. Chahkandi, M. & Ganjali, M., 2009. "On some lifetime distributions with decreasing failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4433-4440, October.
    9. Mahmoudi, Eisa & Jafari, Ali Akbar, 2012. "Generalized exponential–power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4047-4066.
    10. Silva, Rodrigo B. & Barreto-Souza, Wagner & Cordeiro, Gauss M., 2010. "A new distribution with decreasing, increasing and upside-down bathtub failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 935-944, April.
    11. Bagheri, S.F. & Bahrami Samani, E. & Ganjali, M., 2016. "The generalized modified Weibull power series distribution: Theory and applications," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 136-160.
    12. Mahmoudi, Eisa & Sepahdar, Afsaneh, 2013. "Exponentiated Weibull–Poisson distribution: Model, properties and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 76-97.
    13. Francisco Louzada-Neto & Vicente G. Cancho & Gladys D.C. Barriga, 2011. "The Poisson--exponential distribution: a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(6), pages 1239-1248, April.
    14. Idika Eke Okorie & Anthony Chukwudi Akpanta & Johnson Ohakwe & David Chidi Chikezie & Chris Uche Onyemachi & Manoj Kumar Rastogi, 2021. "Zero-Truncated Poisson-Power Function Distribution," Annals of Data Science, Springer, vol. 8(1), pages 107-129, March.
    15. Kuo, Lynn & Yang, Tae Young, 2000. "Bayesian reliability modeling for masked system lifetime data," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 229-241, April.
    16. Al-Mutairi, D.K. & Ghitany, M.E. & Gupta, Ramesh C., 2011. "Estimation of reliability in a series system with random sample size," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 964-972, February.
    17. Abdulhakim A. Al-Babtain & Ibrahim Elbatal & Christophe Chesneau & Farrukh Jamal, 2020. "Box-Cox Gamma-G Family of Distributions: Theory and Applications," Mathematics, MDPI, vol. 8(10), pages 1-24, October.
    18. Daniel Nevo & Reiko Nishihara & Shuji Ogino & Molin Wang, 2018. "The competing risks Cox model with auxiliary case covariates under weaker missing-at-random cause of failure," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 425-442, July.
    19. Kozumi, Hideo, 2004. "Posterior analysis of latent competing risk models by parallel tempering," Computational Statistics & Data Analysis, Elsevier, vol. 46(3), pages 441-458, June.
    20. Mohamed S. Eliwa & Muhammad H. Tahir & Muhammad A. Hussain & Bader Almohaimeed & Afrah Al-Bossly & Mahmoud El-Morshedy, 2023. "Univariate Probability-G Classes for Scattered Samples under Different Forms of Hazard: Continuous and Discrete Version with Their Inferences Tests," Mathematics, MDPI, vol. 11(13), pages 1-24, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:677-686. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.