Research Article
Year 2019,
, 378 - 387, 30.06.2019
Abstract
Son zamanlarda, APT-dağılım ailesi adında yeni bir dağılım ailesi
tanıtılmıştır. Bu dağılım ailesi için üstel dağılım durumunu detaylı bir
şekilde ele alınmıştır. Bu makalede, APT-dağılım ailesinde Pareto dağılımı
çalışılmıştır. APT-Pareto dağılımına ilişkin momentler, hazard fonksiyonu,
yaşam fonksiyonu gibi özellikleri elde edilmiştir. En çok olabilirlik ve en
küçük kareler yöntemleri tartışılmıştır.
Tahmin edicilerin yan ve hata kareler ortalamalarını elde edebilmek için
simülasyon çalışması yapılmıştır. APT-Pareto dağılımının modellemedeki
kullanılabilirliğini göstermek amacıyla gerçek bir veri uygulaması yapılmıştır.
Keywords
References
- Azzalini A., A class of distributions which includes the normal ones, Scandinavian journal of statistics, 24(1985), 171-178.
- Mudholkar G.S. and Srivastava D.K., Exponentiated weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42-2(1993), 299-302.
- Gupta R.C., Gupta P.L. and Gupta R.D., Modeling failure time data by lehman alternatives, Communications in Statistics-Theory and Methods, 27-4(1998), 887-904.
- Gupta R.D. and Kundu D., Exponentiated exponential family: an alternative to gamma and Weibull distributions, Biometrical Journal: Journal of Mathematical Methods in Biosciences, 43-1(2001), 117-130.
- Marshall A.W. and Olkin I., A new method for adding a parameter to a family of distributions with application to the exponential and weibull families, Biometrika, 84-3(1997), 641-652.
- Eugene N., Lee C. and Famoye F., Beta-normal distribution and its applications, Communications in Statistics-Theory and Methods, 31-4(2002), 497-512.
- Alzaatreh A., Lee C. and Famoye F., A new method for generating families of continuous distributions, Metron, 71-1(2013), 63-79.
- Mahdavi A. and Kundu D., A new method for generating distributions with an application to exponential distribution, Communications in Statistics - Theory and Methods, 46-13(2017), 6543-6557.
- Lagarias J.C., Reeds J.A., Wright M.H. and Wright P.E., Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions, SIAM Journal of Optimization, 9-1(1998), 112-147.
- Feigl P. and Zelen M., Estimation of Exponential Survival Probabilities with Concomitant Information, Biometrics, 21-4(1964), 826-838.
- Barreto-Souza W., Santos A.H.S. and Cordeiro G.M., The Beta generalized exponential distribution, Statist. Comput. Simul., 80 (2010), 159-172.
- Nadarajah S. and Kotz S., The Beta exponential distribution, Reliability Engrg. System Safety, 91(2006), 689-697.
- Akinsete A., Famoye F. and Lee C. The Beta-Pareto distribution, Statistics, 42-6(2008), 547-563.
- Gupta R.D. and Kundu D., Generalized exponential distributions, Australian and New Zealand Journal of Statistics, 41-2(1999), 173-188.
- Kus C, A new lifetime distribution, Comput. Statist. Data Anal., 51(2007), 4497-4509.
- Pescim R.R., Dem´etrio 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(2009), 945-957.
- Cooray K. and Ananda M.M.A., A generalization of the half-normal distribution wit applications to lifetime data, Comm. Statist. Theory Methods, 37(2008), 1323-1337.
- Torabi H. and Montazeri N.H., The Gamma-Uniform distribution ans its applications, Kybernetika, 48-1(2012), 16-30.
- Nassar M.M. abd Nada N.K., The beta generalized Pareto distribution, Journal of Statistics: Advances in Theory and Applications, 6(2011), 1-17.
- Burr, I.W., Cumulative frequency functions, Annals of Mathematical Statistics, 13(1942), 215-232.
- Rashwan N.I., A note on Kumaraswamy exponentiated Rayleigh distributioni, Journal of Statistical Theory and Applications, 5(2016), 286-295.
- Paranaíba P.F., Ortega E. M., Cordeiro G. M. and Pescim R.R., The beta Burr XII distribution with application to lifetime data, Computational Statistics and Data Analysis, 55-2(2011), 1118-1136.
- Tahir, M.H., Cordeiro G. M., Mansoor M. and Zubair M., The Weibull-Lomax distribution: properties and applications, Hacettepe Journal of Mathematics and Statistics, 44-2(2015), 461-480.
- Cruz J.N.D., Ortega E.M. and Cordeiro G.M., The log-odd log-logistic Weibull regression model: modelling, estimation, influence diagnostics and residual analysis, Journal of Statistical Computation and Simulation, 86-8(2016), 1516-1538.
- Cordeiro G.M., Gomes A.E., da-Silva C.Q. and Ortega E.M., The beta exponentiated Weibull distribution, Journal of Statistical Computation and Simulation, 83-1(2013), 114-138.
Year 2019,
, 378 - 387, 30.06.2019
Abstract
Recently, the APT-family has been introduced as a new family of
distributions. A special case of this family with exponential distribution is
examined in details. In this paper, Pareto is considered as a baseline
distribution in APT-family. Several properties of the APT-Pareto distribution
such as the moments, hazard rate and survival functions are derived. The
maximum likelihood and least square methods are discussed. Simulation study is
also performed to get the bias and mean square errors of estimates. A numerical
example is given to illustrate the capability of APT-Pareto distribution for
modelling real data.
References
- Azzalini A., A class of distributions which includes the normal ones, Scandinavian journal of statistics, 24(1985), 171-178.
- Mudholkar G.S. and Srivastava D.K., Exponentiated weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42-2(1993), 299-302.
- Gupta R.C., Gupta P.L. and Gupta R.D., Modeling failure time data by lehman alternatives, Communications in Statistics-Theory and Methods, 27-4(1998), 887-904.
- Gupta R.D. and Kundu D., Exponentiated exponential family: an alternative to gamma and Weibull distributions, Biometrical Journal: Journal of Mathematical Methods in Biosciences, 43-1(2001), 117-130.
- Marshall A.W. and Olkin I., A new method for adding a parameter to a family of distributions with application to the exponential and weibull families, Biometrika, 84-3(1997), 641-652.
- Eugene N., Lee C. and Famoye F., Beta-normal distribution and its applications, Communications in Statistics-Theory and Methods, 31-4(2002), 497-512.
- Alzaatreh A., Lee C. and Famoye F., A new method for generating families of continuous distributions, Metron, 71-1(2013), 63-79.
- Mahdavi A. and Kundu D., A new method for generating distributions with an application to exponential distribution, Communications in Statistics - Theory and Methods, 46-13(2017), 6543-6557.
- Lagarias J.C., Reeds J.A., Wright M.H. and Wright P.E., Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions, SIAM Journal of Optimization, 9-1(1998), 112-147.
- Feigl P. and Zelen M., Estimation of Exponential Survival Probabilities with Concomitant Information, Biometrics, 21-4(1964), 826-838.
- Barreto-Souza W., Santos A.H.S. and Cordeiro G.M., The Beta generalized exponential distribution, Statist. Comput. Simul., 80 (2010), 159-172.
- Nadarajah S. and Kotz S., The Beta exponential distribution, Reliability Engrg. System Safety, 91(2006), 689-697.
- Akinsete A., Famoye F. and Lee C. The Beta-Pareto distribution, Statistics, 42-6(2008), 547-563.
- Gupta R.D. and Kundu D., Generalized exponential distributions, Australian and New Zealand Journal of Statistics, 41-2(1999), 173-188.
- Kus C, A new lifetime distribution, Comput. Statist. Data Anal., 51(2007), 4497-4509.
- Pescim R.R., Dem´etrio 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(2009), 945-957.
- Cooray K. and Ananda M.M.A., A generalization of the half-normal distribution wit applications to lifetime data, Comm. Statist. Theory Methods, 37(2008), 1323-1337.
- Torabi H. and Montazeri N.H., The Gamma-Uniform distribution ans its applications, Kybernetika, 48-1(2012), 16-30.
- Nassar M.M. abd Nada N.K., The beta generalized Pareto distribution, Journal of Statistics: Advances in Theory and Applications, 6(2011), 1-17.
- Burr, I.W., Cumulative frequency functions, Annals of Mathematical Statistics, 13(1942), 215-232.
- Rashwan N.I., A note on Kumaraswamy exponentiated Rayleigh distributioni, Journal of Statistical Theory and Applications, 5(2016), 286-295.
- Paranaíba P.F., Ortega E. M., Cordeiro G. M. and Pescim R.R., The beta Burr XII distribution with application to lifetime data, Computational Statistics and Data Analysis, 55-2(2011), 1118-1136.
- Tahir, M.H., Cordeiro G. M., Mansoor M. and Zubair M., The Weibull-Lomax distribution: properties and applications, Hacettepe Journal of Mathematics and Statistics, 44-2(2015), 461-480.
- Cruz J.N.D., Ortega E.M. and Cordeiro G.M., The log-odd log-logistic Weibull regression model: modelling, estimation, influence diagnostics and residual analysis, Journal of Statistical Computation and Simulation, 86-8(2016), 1516-1538.
- Cordeiro G.M., Gomes A.E., da-Silva C.Q. and Ortega E.M., The beta exponentiated Weibull distribution, Journal of Statistical Computation and Simulation, 83-1(2013), 114-138.
There are 25 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | June 30, 2019 |
| Submission Date | October 11, 2018 |
| Acceptance Date | December 19, 2018 |
| Published in Issue | Year 2019 |