A New Distribution Family Constructed By Polynomial Rank Transmutation

In this study, a new polynomial rank transmutation is proposed with the help of thebivariate Farlie-Gumbel Morgenstern distribution family. The distribution familyobtained by this transmutation is considered to be an alternative to the distributionfamilies obtained by quadratic rank transmutation (QRT). Various properties of theintroduced family are studied. Two real data sets are taken into account to show that thisfamily is an alternative to the QRT distribution family.

PDF

___

Al-Aqtash, R., Lee, C., Famoye, F., "Gumbel-weibull distribution: Properties and applications." Journal of Modern Applied Statistical Methods, 13(2), 201-225, (2014).
Alzaatreh, A., Lee, C., Famoye, F., “A new method for generating families of continuous distributions”, Metron, 71(1), 63-79, (2013).
Anderson, T. W., “Anderson–darling tests of goodness-of-fit”, International Encyclopedia of Statistical Science (pp. 52-54), Springer Berlin Heidelberg, (2011).
Andrews, D.F., Herzberg, A.M., “Data: a collection of problems from many fields for the student and research worker”, Springer Science and Business Media, 442 pages, (1985).
Bourguignon, M., Silva, R. B., Cordeiro, G. M., “The Weibull-G family of probability distributions”, Journal of Data Science, 12(1), 53-68. (2014).
Bourguignon, M., Ghosh, I., Cordeiro, G. M., “General results for the transmuted family of distributions and new models”, Journal of Probability and Statistics, Article ID 7208425, 12 pages, http://dx.doi.org/10.1155/2016/7208425. (2016).
Eugene, N., Lee, C., Famoye, F., “The beta-normal distribution and its applications”, Commun. Stat. Theory Methods, 31(4), 497–512, (2002).
Farlie, D.J.G., “The performance of some correlation coefficients for a general bivariate distribution”, Biometrika 47, 307–323, (1960).
Lai, C. D., Xie, M., “A new family of positive quadrant dependent bivariate distributions”, Statistics and probability letters, 46(4), 359-364, (2000).
Marshall, A.W., Olkin, I., “A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families”, Biometrika, 84, 641–652 (1997).
Nadarajah, S., Cordeiro, G. M., Ortega, E. M. “The exponentiated Weibull distribution: a survey”, Statistical Papers, 54(3), 839-877, (2013).
Nichols, C.E., Kane V.E., Browning, M.T., Cagle, G.W., “Northwest Texas Pilot Geochemical Survey”, Union Carbide, Nuclear Division Technical Report (KIUR-l), (1976).
Pogány, T.K., Saboor, A., Provost, S., “The Marshall-Olkin exponential Weibull distribution”, Hacettepe Journal of Mathematics and Statistics, 44(6), 1579, (2015).
Shaw, W.T., Buckley, I.R.C., “The Alchemy of Probability Distributions: Beyond Gram-Charlier & Cornish-Fisher Expansions, and Skew-Normal or Kurtotic-Normal Distributions”, Research report. (2007).
Stephens, M. A., “The Anderson-Darling Statistic”, (No. TR-39). Stanford Univ Ca Dept. of Statistics, (1979).
Yılmaz, M., "A New Family of Distributions with Exponentiated Modified Term", International Journal of Mathematics and StatisticsTM , 18(3), 14-25, (2017).