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A new family of distributions

Year 2017, Volume: 46 Issue: 2, 303 - 314, 01.04.2017

Kadir Karakaya , İsmail Kınacı , Coşkun Kuş , Yunus Akdo‡ğan

Abstract

In this study, a new family of distributions is introduced which is called alpha log-transformation family. We consider a special case of this family with exponential distribution in details. Several properties of the proposed distribution including the raw moments, moment generating function, quantile function and hazard rate function are obtained. Statistical inference is discussed based on complete and progressive censored samples. Simulation study is also performed to observe the performance of the estimates and approximate confidence intervals. A real data is given to illustrate the capability of ALT- Exponential distribution for modelling real data.

Keywords

Confidence intervals Estimation Fisher information Lifetime distribution Progressive censoring

References

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  • Bairamov, I. and Eryılmaz, S. Spacings, exceedances and concomitants in progressive type II censoring scheme. Journal of Statistical Planning and Inference, 136, 527-536, 2006.
  • Balakrishnan, N. and Aggarwala, R. Progressive Censoring: Theory, Methods and Applica- tions. Birkhauser, Boston, 2000.
  • Balakrishnan, N. and Sandhu, R.A. A simple algorithm for generating progressively type-II generated samples, American Statistician, 49, 229-230, 1995.
  • Cooray, K. and Ananda, M. M. A., A generalization of the half-normal distribution with applications to lifetime data, Comm. Statist. Theory Methods, 37, 13231337, 2008.
  • Feigl, P. and Zelen, M., Estimation of exponential survival probabilities with concomitant information., Biometrics 21, 4, 826838, 1965.
  • Gupta, R. D. and Kundu, D., A new class of weighted exponential distributions, Statistics, 43(6), 621634, 2009.
  • Kus, C., A new lifetime distribution, Comput. Statist. Data Anal. 51, 44974509, 2007.
  • Lagarias, J. C., J. A. Reeds, M. H. Wright, and P. E. Wright "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions." SIAM Journal of Optimization. Vol. 9, Number 1, pp. 112147, 1998.
  • Mahdavi, A. and Kundu, D., A new method for generating distributions with an application to exponential distribution, Comm. Statist. Theory Methods, http://dx.doi.org/10.1080/03610926.2015.1130839, In press.
  • Mudholkar, G. S. and Srivastava, D. K., Exponentiated weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42(2), 299302, 1993.
  • Pescim, R. R. , Demetrio, C. G. B., Cordeiro, G.M. , Ortega, E. M. M. and Urbano, M.R., The Beta generalized half-Normal distribution., Comput. Statist. Data Anal., 54, 945957, 2009.
  • Torabi, H. and Montazeri, N.H.,.The Gamma-Uniform Distribution and its applications. Kybernetika, 48(1) 16-30, 2012.

Year 2017, Volume: 46 Issue: 2, 303 - 314, 01.04.2017

Kadir Karakaya , İsmail Kınacı , Coşkun Kuş , Yunus Akdo‡ğan

Abstract

References

  • Akinsete A., Famoye, F. and Lee, C., The Beta-Pareto distribution, Statistics, 42(6), 547- 563, 2008.
  • Bairamov, I. and Eryılmaz, S. Spacings, exceedances and concomitants in progressive type II censoring scheme. Journal of Statistical Planning and Inference, 136, 527-536, 2006.
  • Balakrishnan, N. and Aggarwala, R. Progressive Censoring: Theory, Methods and Applica- tions. Birkhauser, Boston, 2000.
  • Balakrishnan, N. and Sandhu, R.A. A simple algorithm for generating progressively type-II generated samples, American Statistician, 49, 229-230, 1995.
  • Cooray, K. and Ananda, M. M. A., A generalization of the half-normal distribution with applications to lifetime data, Comm. Statist. Theory Methods, 37, 13231337, 2008.
  • Feigl, P. and Zelen, M., Estimation of exponential survival probabilities with concomitant information., Biometrics 21, 4, 826838, 1965.
  • Gupta, R. D. and Kundu, D., A new class of weighted exponential distributions, Statistics, 43(6), 621634, 2009.
  • Kus, C., A new lifetime distribution, Comput. Statist. Data Anal. 51, 44974509, 2007.
  • Lagarias, J. C., J. A. Reeds, M. H. Wright, and P. E. Wright "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions." SIAM Journal of Optimization. Vol. 9, Number 1, pp. 112147, 1998.
  • Mahdavi, A. and Kundu, D., A new method for generating distributions with an application to exponential distribution, Comm. Statist. Theory Methods, http://dx.doi.org/10.1080/03610926.2015.1130839, In press.
  • Mudholkar, G. S. and Srivastava, D. K., Exponentiated weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42(2), 299302, 1993.
  • Pescim, R. R. , Demetrio, C. G. B., Cordeiro, G.M. , Ortega, E. M. M. and Urbano, M.R., The Beta generalized half-Normal distribution., Comput. Statist. Data Anal., 54, 945957, 2009.
  • Torabi, H. and Montazeri, N.H.,.The Gamma-Uniform Distribution and its applications. Kybernetika, 48(1) 16-30, 2012.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Statistics
Authors

Kadir Karakaya

İsmail Kınacı

Coşkun Kuş

Yunus Akdo‡ğan

Publication Date April 1, 2017
Published in Issue Year 2017 Volume: 46 Issue: 2

Cite

APA Karakaya, K., Kınacı, İ., Kuş, C., Akdo‡ğan, Y. (2017). A new family of distributions. Hacettepe Journal of Mathematics and Statistics, 46(2), 303-314.
AMA Karakaya K, Kınacı İ, Kuş C, Akdo‡ğan Y. A new family of distributions. Hacettepe Journal of Mathematics and Statistics. April 2017;46(2):303-314.
Chicago Karakaya, Kadir, İsmail Kınacı, Coşkun Kuş, and Yunus Akdo‡ğan. “A New Family of Distributions”. Hacettepe Journal of Mathematics and Statistics 46, no. 2 (April 2017): 303-14.
EndNote Karakaya K, Kınacı İ, Kuş C, Akdo‡ğan Y (April 1, 2017) A new family of distributions. Hacettepe Journal of Mathematics and Statistics 46 2 303–314.
IEEE K. Karakaya, İ. Kınacı, C. Kuş, and Y. Akdo‡ğan, “A new family of distributions”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 2, pp. 303–314, 2017.
ISNAD Karakaya, Kadir et al. “A New Family of Distributions”. Hacettepe Journal of Mathematics and Statistics 46/2 (April 2017), 303-314.
JAMA Karakaya K, Kınacı İ, Kuş C, Akdo‡ğan Y. A new family of distributions. Hacettepe Journal of Mathematics and Statistics. 2017;46:303–314.
MLA Karakaya, Kadir et al. “A New Family of Distributions”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 2, 2017, pp. 303-14.
Vancouver Karakaya K, Kınacı İ, Kuş C, Akdo‡ğan Y. A new family of distributions. Hacettepe Journal of Mathematics and Statistics. 2017;46(2):303-14.

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