On Beta-Akash distribution with applications

In this paper, a Beta-Akash distribution that extends the Akash distribution has been introduced. Expansions for the cumulative distribution and probability density functions of the new distribution are given. Various properties of the new distribution such as hazard function, moments, cumulants, skewness, kurtosis, mean deviations, Bonferroni and Lorenz curves, R݁́nyi  and Tsallis entropies, and stress-strength reliability are discussed. Moment generating function and characteristic function of the new model were derived. Distribution and the moment of order statistic have been derived. The method of maximum likelihood was used for estimation of parameters. The new model is quite flexible in analysing positively skewed data. A real life data was used to demonstrate the flexibility of the new distribution

Akinsete, A. and Lowe, C. (2009). Beta-Rayleigh distribution in reliability measure, Section on Physical and Engineering Sciences. In: Proceedings of the American Statistical Association, 1, 3103-3107.

Akinsete, A., Famoye, F. and Lee, C. (2008). The Beta-Pareto distribution, Statistics, Comput. Math. Appl., 42(6), 547-563.

Alshawarbeh, E., Lee, C. and Famoye, F. (2012). The Beta-Cauchy distribution, J. Probab. Statist. Sci., 10, 41-57.

Amusan, G.E. (2010). The Beta Maxwell distribution. Master's Thesis, Marsh. Digit. Schol.Stat.

Bonferroni, C.E. (1930). Elementi di Statistica Generale. Seeber, Firenze.

Castellares, F., Montenegro, L.C. and Cordeiro, G.M. (2011). The beta lognormal distribution, J. Statist. Computat. Simul., 83, 203-228.

Cordeiro, G.M. and Lemonte, A.J. (2011a). The beta Laplace distribution, Stat. Probab. Lett., 81, 973-982.

Cordeiro, G.M. and Lemonte, A.J. (2011b). The Beta-Birnbaum-Saunders distribution: an improved distribution for fatigue life modelling. Computat, Stat. Data Anal., 55(3),1445-1461.

Cordeiro, G.M., Gomes, A.E., Da-Silva, C.Q. and Ortega, E.M.M. (2013). The Beta
exponentiated Weibull distribution, Statist. Papers, 83(1), 114-138.

Cordeiro, G.M., Nobre, J.S., Pescim, R.R. and Ortega, E.M.M. (2012). The beta Moyal: A useful-skew distribution, Int. J. Res. Rev. Appl. Sci., 10(2), 171-192.

Dias, C.R., Alizadeh, M. and Cordeiro, G.M. (2018). The beta Nadarajah-Haghighi distribution, Hacet. J. Math. Stat., 47, 1302-1320.

Domma, F. and Condino, F. (2013). The Beta-Dagum distribution. Comm. Stat.– Theo. Meth., 42(22), 4070–4090.

Enogwe, S.U., Nwosu, D.F., Ngome, E.C, Onyekwere, C.K. and Omeje, I.L. (2020). Twoparameter Odoma distribution with applications, Journal of Xidian University,
14(8), 740-764.

Eugene, N., Lee, C. and Famoye, F. (2002). Beta-normal distribution and its Applications, Communications in Statistics: Theory and Methods, 31, 497-512.

Famoye, F., Lee, C. and Olumolade, O. (2005). The Beta-Weibull Distribution, J. Stat. Theo. Appl., 4(2), 121-136.

Fischer, M.J. and Vaughan, D. (2016). The beta-hyperbolic secant distribution, Austrian J. Stat., 39(3), 245-258.

Gomes, A.E., Da-Silva, C.Q., Cordeiro, G.M. and Ortega, E.M.M. (2013). The beta Burr III model for lifetime data, Brazilian J. Probab. Stat., 27(4), 502-543.

Gupta, A.K. and Nadarajah, S. (2006). Beta Bessel distribution, Int. J. Math. Mathemat. Sci. 56, 161, 1-14.

Jafari, A.A., Tahmasebi, S. and Alizadeh, M. (2014). The beta-Gompertz distribution, Revista Colombiana de Estadstica, 37(1), 141-158.

Lehmann, L.E. and Casella, G. (1998). Theory of point estimation, 2nd edition, Springer, New York.

Merovci, F., Khalee, M.A., Ibrahim, N.A. and Shitan, M. (2016). The beta Burr Type X distribution: properties with application, Springer Plus, 5(1), 1-18.

Mir Mostafaee, S.M.T.K., Mahdizadeh, M. and Nadarajah, S. (2015). The beta Lindley distribution, J. Data Sci., 13, 603-626.

Nadarajah, S. and Kotz, S. (2006). The beta exponential distribution, Reliab. Eng. Syst. Saf., 91, 689-697.

Nadarajah, S. and Gupta, A.K. (2004). The Beta-Frechet distribution, Far East J. Theoret. Stat., 14, 15-24.

Nadarajah, S. and Kotz, S. (2004). The beta Gumbel distribution, Math. Prob. Eng., 4, 323- 332.

Okereke E.W. and Uwaeme O.R. (2018). Exponentiated Akash distribution and its applications, J. Nig. Stat. Asso., 30, 1-13.

Ownuk, J. (2015). The Beta exponentiated Gumbel distribution, JIRSS 14(2), 1-14.

Rényi,, A. (1961). On measures of entropy and information, Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, I, 547 - 561.

Rodrigues, J.A., Silva, A.P.C.M. and Hamedani, G.G. (2015). The beta exponentiated Lindley distribution, J. Statist. Theo. Appl., 14(1), 60-75.

Shanker R. and Fesshaye, H. (2016). On modeling of lifetime data using one parameter Akash,

Shanker, Lindley and exponential distributions, Biom. Biostat. Int. J. 3(6), 1-12.

Shanker R. and K.K. Shukla, (2017). Power Akash distribution and its application, J. Appl. Quant. Meth. 12, 1-10.

Shukla, K.K., Shanker, R. and Pratap, A. (2018). A generalized Akash distribution, Biom. Biostat. Int. J. 7(1), 18-26.

Shanker, R. (2015). Akash distribution and its applications, Internet. J. Prob. Stat. 4(3), 65-75.

Shanker, R. (2016). A quasi Akash distribution, Assam Stat. Rev. 30 (1), 135-160.

Shanker, R. and K.K. Shukla, On two-parameter Akash distribution, Biom Biostat. Int. J. 6 (2017), 416-425.

Shanker, R. and Shukla, K.K. (2017). On two-parameter Akash distribution, Biometrics and Biostatistics International Journal, 7, 416-425.

Shittu, O.I. and Adepoju, K.A. (2012). On the Beta-Nakagami distribution, Prog. Appl. Math.,5(1), 49-58.

Souza, W.B., Santos, A.H. and Cordeiro, G.M. (2010). The beta generalized exponential distribution, J. Stat. Comput. Simul., 80, 159-172.

Weisberg, S. (2005). Applied linear regression, 3rd edition, Wiley and sons, Inc, New York.