Research Article
Year 2019,
Volume: 40 Issue: 2, 493 - 504, 30.06.2019
Abstract
In this paper, the ratio of maximized likelihood and
Minimized Kullback-Leibler Divergence methods are discussed for discrimination
between log-normal and Weibull distributions. The progressive Type-II right
censored sample is considered in the study. The probability of correct
selections is simulated and compared to investigate the performance of the
procedures for different censoring schemes and parameter settings.
Keywords
Discrimination Log-normal distribution Power analysis Simulation Progressive type-II right censoring
References
- Alzaid A. and Sultan, K.S., Discriminating between gamma and lognormal distributions with applications. Journal of King Saud University - Science, 21-2 (2009) 99-108.
- Kundu D. and Manglick, A., Discriminating between the log-normal and gamma distributions. Journal of the Applied Statistical Sciences, 14 (2005) 175-187.
- Bromideh A.A. and Valizadeh R., Discrimination between Gamma and Log-Normal Distributions by Ratio of Minimized Kullback-Leibler Divergence. Pakistan Journal of Statistics and Operation Research, 9-4 (2014) 443-453.
- Dey A.K. and Kundu D., Discriminating among the log-normal, Weibull, and generalized exponential distributions. IEEE Transactions on reliability, 58-3 (2009) 416-424.
- Dey A.K., and Kundu, D., Discriminating between the log-normal and log-logistic distributions. Communications in Statistics-Theory and Methods, 39-2 (2009) 280-292.
- Kundu D., Discriminating between normal and Laplace distributions. In Advances in Ranking and Selection, Multiple Comparisons, and Reliability, Springer (2005) 65-79.
- Kantam R. R., Priya M., and Ravikumar M., Likelihood ratio type test for linear failure rate distribution vs. exponential distribution. Journal of Modern Applied Statistical Methods, 13-1 (2014) 11.
- Ngom P., Nkurunziza J.D.D., and Ogouyandjou C.S., Discriminating between two models based on Bregman divergence in small samples, (2017).
- Ravikumar M. and Kantam R., Discrimination Between Burr Type X Distribution Versus Log-Logistic and Weibull-Exponential Distributions. i-Manager's Journal on Mathematics, 5-4 (2017) 39.
- Qaffou A. and Zoglat A., Discriminating Between Normal and Gumbel Distributions. REVSTAT-Statistical Journal, 15-4 (2017) 523-536.
- Algamal Z., Using maximum likelihood ratio test to discriminate between the inverse gaussian and gamma distributions. International Journal of Statistical Distributions, 1-1 (2017) 27-32.
- Quesenberry C.P., and Kent J., Selecting among Probability Distributions Used in Reliability. Technometrics, 24-1 (1982) 59-65.
- Dumonceaux R., and Antle C.E., Discrimination between the log-normal and the Weibull distributions. Technometrics, 15-4 (1973) 923-926.
- Pasha G., Shuaib K.M., and Pasha A. H., Discrimination between Weibull and Log-Normal Distributions For Lifetime data. Journal of Research (Science), Bahauddin Zakariya University, Multan, Pakistan, 17-2 (2006) 103-114.
- Bromideh A.A., Discriminating between Weibull and log-normal distributions based on Kullback-Leibler divergence. Ekonometri ve İstatistik e-Dergisi, 16 (2012) 44-54.
- Raqab M.Z., Al-Awadhi S.A., and Kundu D., Discriminating among Weibull, log-normal, and log-logistic distributions. Communications in Statistics-Simulation and Computation, 47-5 (2018) 1397-1419.
- Elsherpieny M.R., On Discriminating between Gamma and Log-logistic Distributions in Case of Progressive Type II Censoring, Pak.j.stat.oper.res. 13-1 (2017) 157-183.
- Kundu D. and Manglick A., Discriminating between the Weibull and Log-Normal Distributions, 51-6 (2004) 893-905.
- Dey A.K. and Kundu D., Discriminating between the Weibull and Log-normal distributions for type-II censored data, Statistics, 46-2 (2012) 197-214
- Kim J.S. and Yum B.J., Selection between Weibull and lognormal distributions: A comparative simulation study. Computational Statistics & Data Analysis, 53-2 (2008) 477-485.
- Bairamov I.G.. and Eryılmaz S., Spaciings, exceedances and concomitants in progressive type II censoring scheme. Journal of Statistical Planning and inference, 136 (2006) 527-536.
- Balakrishnan N. and Aggarwala R., Progressive Censoring: Theory, Methods and Applications, Statistics for Industry and Technology, Birkhauser, (2000).
- Saraçoğlu, B., Kınacı, İ., Kundu, D., " On Estimation of R = P(Y < X) for Exponential Distribution Under Progressive Type-II Censoring ",82 (5), , 729-744, 2012
- Akdam, N., Kinaci, I., Saracoglu, B., "Statistical inference of stress-strength reliability for the exponential power (EP) distribution based on progressive type-II censored samples ", Hacettepe Journal Of Mathematics and Statistics, 46 239-253 2017.
- Demir, E., Saracoglu, B., "Maximum Likelihood Estimation for the Parameters of the Generalized Gompertz Distribution under Progressive Type-II Right Censored Samples ", Journal of Selcuk University Natural and Applied Science, 4 (2015) 41-48.
- Singh S. Tripathi, M.T. and Wu S.J., On estimating parameters of a progressively censored lognormal distribution, Journal of Statistical Computation and Simulation, 85-6 (2015) 1071-1089.
- Wu S.J., Estimation of the Parameters of the Weibull Distribution with Progressively Censored Data, Journal of the Japan Statistical Society, 32-2 (2002) 155-163.
- Mahdizadeh M. and Zamanzade E., New goodness of fit tests for the Cauchy distribution, Journal of Applied Statistics, 44-6 (2017) 1106-1121.
- Burnham K.P. and Anderson D.R., "Model selection and multimodel inference: a practical information-theoretic approach," 2nd eds., Springer, New York. (2002).
- Lieblein J. and Zelen M., Statistical Investigation of the Fatigue Life of Deep-Groove Ball Bearings. Journal of Research of the National Bureau of Standards, 57-5 (1956) 273-315.
- Viveros R. and Balakrishnan N., Interval Estimation of Parameters of Life From Progressively Censored Data, Technometrics, 36-1 (1994) 84-91.
Year 2019,
Volume: 40 Issue: 2, 493 - 504, 30.06.2019
Abstract
Bu çalışmada, log-normal ve weibull dağılımları arasında ayırım için en
çok olabilirlik oran ve Kullback-Leibler uzaklık metotları tartışılmıştır.
Çalışmada, ilerleyen tür sansürlü veri durumu ele alınmıştır. Doğru seçim
oranları hesaplanmış ve farklı parametre ve sansür şemaları altında testlerin
performansları karşılaştırılmıştır.
References
- Alzaid A. and Sultan, K.S., Discriminating between gamma and lognormal distributions with applications. Journal of King Saud University - Science, 21-2 (2009) 99-108.
- Kundu D. and Manglick, A., Discriminating between the log-normal and gamma distributions. Journal of the Applied Statistical Sciences, 14 (2005) 175-187.
- Bromideh A.A. and Valizadeh R., Discrimination between Gamma and Log-Normal Distributions by Ratio of Minimized Kullback-Leibler Divergence. Pakistan Journal of Statistics and Operation Research, 9-4 (2014) 443-453.
- Dey A.K. and Kundu D., Discriminating among the log-normal, Weibull, and generalized exponential distributions. IEEE Transactions on reliability, 58-3 (2009) 416-424.
- Dey A.K., and Kundu, D., Discriminating between the log-normal and log-logistic distributions. Communications in Statistics-Theory and Methods, 39-2 (2009) 280-292.
- Kundu D., Discriminating between normal and Laplace distributions. In Advances in Ranking and Selection, Multiple Comparisons, and Reliability, Springer (2005) 65-79.
- Kantam R. R., Priya M., and Ravikumar M., Likelihood ratio type test for linear failure rate distribution vs. exponential distribution. Journal of Modern Applied Statistical Methods, 13-1 (2014) 11.
- Ngom P., Nkurunziza J.D.D., and Ogouyandjou C.S., Discriminating between two models based on Bregman divergence in small samples, (2017).
- Ravikumar M. and Kantam R., Discrimination Between Burr Type X Distribution Versus Log-Logistic and Weibull-Exponential Distributions. i-Manager's Journal on Mathematics, 5-4 (2017) 39.
- Qaffou A. and Zoglat A., Discriminating Between Normal and Gumbel Distributions. REVSTAT-Statistical Journal, 15-4 (2017) 523-536.
- Algamal Z., Using maximum likelihood ratio test to discriminate between the inverse gaussian and gamma distributions. International Journal of Statistical Distributions, 1-1 (2017) 27-32.
- Quesenberry C.P., and Kent J., Selecting among Probability Distributions Used in Reliability. Technometrics, 24-1 (1982) 59-65.
- Dumonceaux R., and Antle C.E., Discrimination between the log-normal and the Weibull distributions. Technometrics, 15-4 (1973) 923-926.
- Pasha G., Shuaib K.M., and Pasha A. H., Discrimination between Weibull and Log-Normal Distributions For Lifetime data. Journal of Research (Science), Bahauddin Zakariya University, Multan, Pakistan, 17-2 (2006) 103-114.
- Bromideh A.A., Discriminating between Weibull and log-normal distributions based on Kullback-Leibler divergence. Ekonometri ve İstatistik e-Dergisi, 16 (2012) 44-54.
- Raqab M.Z., Al-Awadhi S.A., and Kundu D., Discriminating among Weibull, log-normal, and log-logistic distributions. Communications in Statistics-Simulation and Computation, 47-5 (2018) 1397-1419.
- Elsherpieny M.R., On Discriminating between Gamma and Log-logistic Distributions in Case of Progressive Type II Censoring, Pak.j.stat.oper.res. 13-1 (2017) 157-183.
- Kundu D. and Manglick A., Discriminating between the Weibull and Log-Normal Distributions, 51-6 (2004) 893-905.
- Dey A.K. and Kundu D., Discriminating between the Weibull and Log-normal distributions for type-II censored data, Statistics, 46-2 (2012) 197-214
- Kim J.S. and Yum B.J., Selection between Weibull and lognormal distributions: A comparative simulation study. Computational Statistics & Data Analysis, 53-2 (2008) 477-485.
- Bairamov I.G.. and Eryılmaz S., Spaciings, exceedances and concomitants in progressive type II censoring scheme. Journal of Statistical Planning and inference, 136 (2006) 527-536.
- Balakrishnan N. and Aggarwala R., Progressive Censoring: Theory, Methods and Applications, Statistics for Industry and Technology, Birkhauser, (2000).
- Saraçoğlu, B., Kınacı, İ., Kundu, D., " On Estimation of R = P(Y < X) for Exponential Distribution Under Progressive Type-II Censoring ",82 (5), , 729-744, 2012
- Akdam, N., Kinaci, I., Saracoglu, B., "Statistical inference of stress-strength reliability for the exponential power (EP) distribution based on progressive type-II censored samples ", Hacettepe Journal Of Mathematics and Statistics, 46 239-253 2017.
- Demir, E., Saracoglu, B., "Maximum Likelihood Estimation for the Parameters of the Generalized Gompertz Distribution under Progressive Type-II Right Censored Samples ", Journal of Selcuk University Natural and Applied Science, 4 (2015) 41-48.
- Singh S. Tripathi, M.T. and Wu S.J., On estimating parameters of a progressively censored lognormal distribution, Journal of Statistical Computation and Simulation, 85-6 (2015) 1071-1089.
- Wu S.J., Estimation of the Parameters of the Weibull Distribution with Progressively Censored Data, Journal of the Japan Statistical Society, 32-2 (2002) 155-163.
- Mahdizadeh M. and Zamanzade E., New goodness of fit tests for the Cauchy distribution, Journal of Applied Statistics, 44-6 (2017) 1106-1121.
- Burnham K.P. and Anderson D.R., "Model selection and multimodel inference: a practical information-theoretic approach," 2nd eds., Springer, New York. (2002).
- Lieblein J. and Zelen M., Statistical Investigation of the Fatigue Life of Deep-Groove Ball Bearings. Journal of Research of the National Bureau of Standards, 57-5 (1956) 273-315.
- Viveros R. and Balakrishnan N., Interval Estimation of Parameters of Life From Progressively Censored Data, Technometrics, 36-1 (1994) 84-91.
There are 31 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | June 30, 2019 |
| Submission Date | October 12, 2018 |
| Acceptance Date | December 19, 2018 |
| Published in Issue | Year 2019Volume: 40 Issue: 2 |