Description Details Author(s) References

Developed for computing the probability density function, computing the cumulative distribution function, computing the quantile function, random generation, and estimating the parameters of 24 G-family of statistical distributions via the maximum product spacing approach introduced in <https://www.jstor.org/stable/2345411>. These families are: beta G distribution due to Eugene et al. (2002), beta exponential G distribution due to Alzaatreh et al. (2013), beta extended G distribution due to Alzaatreh et al. (2013), exponentiated G distribution due to Gupta et al. (1998), exponentiated Kumaraswamy G distribution due to Lemonte et al. (2013), exponentiated exponential Poisson G distribution due to Ristic and Nadarajah (2014), exponentiated generalized G distribution due to Cordeiro et al. (2013), gamma type I G distribution due to Zografos and Balakrishnan (2009), gamma type II G distribution due to Ristic and Balakrishnan (2012), gamma uniform G distribution due to Torabi and Montazeri (2012), gamma-X generated of log-logistic family of G distribution due to Alzaatreh et al. (2013), gamma-X family of modified beta exponential G distribution due to Alzaatreh et al. (2013), geometric exponential Poisson G distribution due to Nadarajah et al. (2013), generalized beta G distribution due to Alexander et al. (2012), generalized transmuted G distribution due to Merovci et al. (2017), Kumaraswamy G distribution due to Cordeiro and Castro (2011), log gamma type I G distribution due to Amini et al. (2013), log gamma type II G distribution due to Amini et al. (2013), Marshall-Olkin G distribution due to Marshall and Olkin (1997), Marshall-Olkin Kumaraswamy G distribution due to Roshini and Thobias (2017), modified beta G distribution due to Nadarajah et al. (2013), odd log-logistic G distribution due to Gauss et al. (2017), truncated-exponential skew-symmetric G distribution due to Nadarajah et al. (2014), and Weibull G distribution due to Alzaatreh et al. (2013).

Package: MPS

Type: Package

Version: 2.3.1

Date: 2019-09-04

License: GPL(>=2)

Mahdi Teimouri and Saralees Nadarajah

Maintainer: Mahdi Teimouri <teimouri@aut.ac.ir>

Alexander, C., Cordeiro, G. M., and Ortega, E. M. M. (2012). Generalized beta-generated distributions, *Computational Statistics and Data Analysis*, 56, 1880-1897.

Alzaatreh, A., Lee, C., and Famoye, F. (2013). A new method for generating families of continuous distributions, *Metron*, 71, 63-79.

Amini, M., MirMostafaee, S. M. T. K., and Ahmadi, J. (2013). Log-gamma-generated families of distributions, *Statistics*, 48 (4), 913-932.

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Cordeiro, G. M. and Castro, M. (2011). A new family of generalized distributions, *Journal of Statistical Computation and Simulation*, 81, 883-898.

Cordeiro, G. M., Ortega, E. M. M., and da Cunha, D. C. C. (2013). The exponentiated generalized class of distributions, *Journal of Data Science*, 11, 1-27.

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Gupta, R. C., Gupta, P. L., and Gupta, R. D. (1998). Modeling failure time data by Lehman alternatives, *Communications in Statistics-Theory and Methods*, 27, 887-904.

Gauss, M. C., Alizadeh, M., Ozel, G., Hosseini, B. Ortega, E. M. M., and Altunc, E. (2017). The generalized odd log-logistic family of distributions: properties, regression models and applications, *Journal of Statistical Computation and Simulation*, 87(5), 908-932.

Lemonte, A. J., Barreto-Souza, W., and Cordeiro, G. M. (2013). The exponentiated Kumaraswamy distribution and its log-transform, *Brazilian Journal of Probability and Statistics*, 27, 31-53.

Marshall, A. W. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, *Biometrika*, 84, 641-652.

Merovcia, F., Alizadeh, M., Yousof, H. M., and Hamedani, G. G. (2017). The exponentiated transmuted-G family of distributions: Theory and applications, *Communications in Statistics-Theory and Methods*, 46(21), 10800-10822.

Nadarajah, S., Cancho, V. G., and Ortega, E. M. M. (2013). The geometric exponential Poisson distribution, *Statistical Methods & Applications*, 22, 355-380.

Nadarajah, S., Teimouri, M., and Shih, S. H. (2014). Modified beta distributions, *Sankhya*, 76 (1), 19-48.

Nadarajah, S., Nassiri, V., and Mohammadpour, A. (2014). Truncated-exponential skew-symmetric distributions, *Statistics*, 48 (4), 872-895.

Ristic, M. M. and Balakrishnan, N. (2012). The gamma exponentiated exponential distribution, *Journal of Statistical Computation and Simulation*, 82, 1191-1206.

Ristic, M. M. and Nadarajah, S. (2014). A new lifetime distribution, *Journal of Statistical Computation and Simulation*, 84 (1), 135-150.

Roshini, G. and Thobias, S. (2017). Marshall-Olkin Kumaraswamy Distribution, *International Mathematical Forum*, 12 (2), 47-69.

Torabi, H. and Montazeri, N. H. (2012). The gamma uniform distribution and its applications, *Kybernetika*, 48, 16-30.

Zografos, K. and Balakrishnan, N. (2009). On families of beta- and generalized gamma-generated distributions and associated inference, *Statistical Methodology*, 6, 344-362.

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