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The modified Weibull geometric distribution

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  • Min Wang
  • Ibrahim Elbatal

Abstract

A new class of lifetime distributions is introduced by compounding the modified Weibull and geometric distributions, the so-called modified Weibull geometric distribution. It includes as special submodels such as linear failure rate geometric distribution, Weibull geometric distribution, exponential geometric distribution, among others. We study its structural properties including probability density function, hazard functions, moments, generating and quantile functions. The distribution is capable of monotonically increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rates. Estimation by maximum likelihood and inference for a large sample are presented. An expectation-maximization algorithm is used to determine the maximum likelihood estimates of the parameters. Finally, a real data set is analyzed for illustrative purposes. Copyright Sapienza Università di Roma 2015

Suggested Citation

  • Min Wang & Ibrahim Elbatal, 2015. "The modified Weibull geometric distribution," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 303-315, December.
    • Handle: RePEc:spr:metron:v:73:y:2015:i:3:p:303-315
    DOI: 10.1007/s40300-014-0052-1
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    References listed on IDEAS

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    1. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
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    4. 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.
    5. Adamidis, Konstantinos & Dimitrakopoulou, Theodora & Loukas, Sotirios, 2005. "On an extension of the exponential-geometric distribution," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 259-269, July.
    6. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
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    Cited by:

    1. Gauss M. Cordeiro & Giovana O. Silva & Edwin M. M. Ortega, 2016. "An extended-G geometric family," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-16, December.
    2. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.

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