Exponentiated Transmuted Power Function Distribution: Theory & Applications

Rana USMAN [1] , Muhammad Ahsan ul HAQ [2] , Nurbanu BURSA [3] , Gamze ÖZEL [4]

111 161

This paper introduces a new generalization of Transmuted Power Function distribution named as Exponentiated Transmuted Power Function distribution with its fundamental properties. The expressions of failure and survival rate functions on the basis of their graphs are provided. We compute moments, moment generating function, quantile function. Then, Rényi entropy is discussed and the expressions of the order statistics are derived.  Parameters of the proposed distribution are estimated using the maximum likelihood method. Real lifetime data application shows the flexibility of the proposed distribution and its better fit as compared to some existing models.

Transmuted power function distribution, power function distribution, Rényi entropy, maximum likelihood estimation
  • Ahsanullah, M., & Kabir, A. L. (1974). A characterization of the power function distribution. The Canadian Journal of Statistics/La Revue Canadienne de Statistique, 95-98. Ahsanullah, M. (1989). Estimation of the parameters of a power function distribution by record values. Pakistan Journal of Statistics, 5(2), 189-194. Ali, M. M., & Woo, J. (2005). Inference on reliability P (Y< X) in a power function distribution. Journal of Statistics and Management Systems, 8(3), 681-686. Balakrishnan, N., & Nevzorov, V. (2003). A primer on statistical distributions. Hoboken, New Jersey: A John Wiley & Sons: Inc. Bursa, N., & Ozel, G. (2017). The exponentiated Kumaraswamy-power function distribution. Hacettepe Journal of Mathematics and Statistics, 46(2), 277-292. Cordeiro, G. M., & dos Santos Brito, R. (2012). The beta power distribution. Brazilian Journal of Probability and Statistics, 26(1), 88-112. Cox D.R., & Lewis P.A.W. (1966). The Statistical Analysis of Series of Events, Methuen.
  • Forbes, C., Evans, M., Hastings, N., & Peacock, B. (2011). Statistical distributions: John Wiley & Sons. Haq, M., Usman, R., & Fateh, A. (2016a). A study on Kumaraswamy power function distribution. Submitted to Kuwait Journal of Science. Haq, M. A., Butt, N. S., Usman, R. M., & Fattah, A. A. (2016b). Transmuted power function distribution. Gazi University Journal of Science, 29(1), 177-185. Johnson, R. A. (1994). Miller and Freund's Probability and Statistics for Engineers: Prentice Hall. Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, vol. 2 of Wiley series in probability and mathematical statistics: applied probability and statistics: Wiley, New York. Meniconi, M., & Barry, D. (1996). The power function distribution: A useful and simple distribution to assess electrical component reliability. Microelectronics Reliability, 36(9), 1207-1212. Merovci, F. (2016). Transmuted rayleigh distribution. Austrian Journal of Statistics, 42(1), 21-31. Oguntunde, P., & Adejumo, O. (2014). The transmuted inverse exponential distribution. International Journal of Advanced Statistics and Probability, 3(1), 1-7. Shakeel, M., ul Haq, M. A., Hussain, I., Abdulhamid, A. M., & Faisal, M. (2016). Comparison of two new robust parameter estimation methods for the power function distribution. PloS One, 11(8), 1-11. Sultan, R., Sultan, H., & Ahmad, S. (2014). Bayesian analysis of power function distribution under double priors. Journal of Statistics Applications & Probability, 3(2), 239. Tahir, M., Alizadeh, M., Mansoor, M., Cordeiro, G. M., & Zubair, M. (2014). The Weibull-power function distribution with applications. Hacettepe Journal of Mathematics and Statistics. Zaka, A., & Akhter, A. S. (2013). Methods for estimating the parameters of the power function distribution. Pakistan Journal of Statistics and Operation Research, 9(2), 1-12.
Konular
Dergi Bölümü Statistics
Yazarlar

Yazar: Rana USMAN
Kurum: University of Okara
Ülke: Pakistan


Yazar: Muhammad Ahsan ul HAQ
Kurum: University of the Punjab
Ülke: Pakistan


Yazar: Nurbanu BURSA
Ülke: Turkey


Yazar: Gamze ÖZEL
Ülke: Turkey


Bibtex @araştırma makalesi { gujs310862, journal = {Gazi University Journal of Science}, issn = {}, eissn = {2147-1762}, address = {Gazi Üniversitesi}, year = {}, volume = {31}, pages = {660 - 675}, doi = {}, title = {Exponentiated Transmuted Power Function Distribution: Theory \& Applications}, key = {cite}, author = {USMAN, Rana and BURSA, Nurbanu and HAQ, Muhammad Ahsan ul and ÖZEL, Gamze} }
APA USMAN, R , HAQ, M , BURSA, N , ÖZEL, G . (). Exponentiated Transmuted Power Function Distribution: Theory & Applications. Gazi University Journal of Science, 31 (2), 660-675. Retrieved from http://dergipark.gov.tr/gujs/issue/37206/310862
MLA USMAN, R , HAQ, M , BURSA, N , ÖZEL, G . "Exponentiated Transmuted Power Function Distribution: Theory & Applications". Gazi University Journal of Science 31 (): 660-675 <http://dergipark.gov.tr/gujs/issue/37206/310862>
Chicago USMAN, R , HAQ, M , BURSA, N , ÖZEL, G . "Exponentiated Transmuted Power Function Distribution: Theory & Applications". Gazi University Journal of Science 31 (): 660-675
RIS TY - JOUR T1 - Exponentiated Transmuted Power Function Distribution: Theory & Applications AU - Rana USMAN , Muhammad Ahsan ul HAQ , Nurbanu BURSA , Gamze ÖZEL Y1 - 2018 PY - 2018 N1 - DO - T2 - Gazi University Journal of Science JF - Journal JO - JOR SP - 660 EP - 675 VL - 31 IS - 2 SN - -2147-1762 M3 - UR - Y2 - 2018 ER -
EndNote %0 Gazi University Journal of Science Exponentiated Transmuted Power Function Distribution: Theory & Applications %A Rana USMAN , Muhammad Ahsan ul HAQ , Nurbanu BURSA , Gamze ÖZEL %T Exponentiated Transmuted Power Function Distribution: Theory & Applications %D 2018 %J Gazi University Journal of Science %P -2147-1762 %V 31 %N 2 %R %U
ISNAD USMAN, Rana , HAQ, Muhammad Ahsan ul , BURSA, Nurbanu , ÖZEL, Gamze . "Exponentiated Transmuted Power Function Distribution: Theory & Applications". Gazi University Journal of Science 31 / 2 660-675.