The Mc-$\Gamma$ Distribution and Its Statistical Properties: An Application to Reliability Data

  •  Francisco W. P. Marciano    
  •  A. D. C. Nascimento    
  •  M. Santos-Neto    
  •  G. M. Cordeiro    


The gamma distribution has been widely used in many research areas such as engineering, hydrology and survival analysis. We propose a new distribution, called the McDonald gamma distribution, which presents greater flexibility to model scenarios involving non-negative data. The new density function is re\-pre\-sen\-ted as a double linear combination of gamma densities. We also propose analytical expressions for some mathematical quantities: moments, moment ge\-ne\-ra\-ting function, log-moment, mean deviations, {Lorentz} and Bonferroni curves, order statistics, entropy and quantile function. The score function and the observed information matrix of this new distribution are derived. A real data set is used to illustrate the importance of the proposed model.

This work is licensed under a Creative Commons Attribution 4.0 License.
  • ISSN(Print): 1927-7032
  • ISSN(Online): 1927-7040
  • Started: 2012
  • Frequency: bimonthly

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