تعمیم هایی از اطلاع کولبک-لیب لر بر اساس تابع بقا

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه آمار، دانشگاه بیرجند، بیرجند، ایران

چکیده

در این مقاله ابتدا به برخی از تعمیم های اطلاع کولبک-لیبلر و خواص آن ها پرداخته می شود. سپس
شرایط گشتاوری برای توزیع ماکسیمم آنتروپی مانده ی تجمعی بررسی و رابطه ی بین اطلاع کولبک-لیبلر مانده ی تجمعی
مطالعه می شود. همچنین در مورد روش های برآورد پارامتر مقیاس توزیع (CRE) و آنتروپی مانده ی تجمعی (CRKL)
رایلی بحث شده و دو روش برآورد آن ارائه می شود. در ادامه اطلاع کولبک-لیبلر مانده ی تجمعی را به عنوان یک آماره
آزمون نیکویی برازش به کار برده و سپس مقادیر بحرانی و توان آزمون های پیشنهادی محاسبه و با توان سایر آزمون ها
مقایسه می شود. در پایان، آزمون ها برای یک مجموعه داده ی واقعی به کار گرفته می شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Some extensions of Kullback-Leibler information based on survival function

نویسندگان [English]

  • Hedieh Eftekhari Moodi
  • Hadi Alizadeh Noughabi
  • Mohammad Khorashadizadeh
Department of Statistics, University of Birjand, Birjand , Iran
چکیده [English]

In this article, we first investigate some extensions of Kullback-Leibler information and their
properties. Then, we consider the moment constraints for the maximum distribution of cumulative residual
entropy and investigate the relationship between the cumulative residual Kullback-Leibler information
(CRKL) and cumulative residual entropy (CRE). We also discuss the methods for estimating the scale
parameter of Rayleigh distribution and provide two estimation methods. In the following we use cumulative
residual Kullback-Leibler information as a goodness of fit test statistic. Then we compute the critical
values and the power of proposed tests and compare the power values with with the power of other tests.
Finally, we apply the tests for a real data set.

کلیدواژه‌ها [English]

  • Goodness of fit test
  • Cumulative residual entropy
  • Kullback-Leibler information
  • Cumulative residual Kullback-Leibler information
  • Power of test
  • Mont Carlo simulation
[1] Alizadeh Noughabi, R., & Alizadeh Noughabi, H., & Ebrahimi Moghaddam Behabadi, A., (2014) . An entropy test for the Rayleigh distribution and power comparison. Journal of Statistical Computation and Simulation, 84 , 151-158 .
[2] Anderson, T.W., & Darling, D.A., (1954) . A test of goodness of fit. Journal of American Statistical Association, 49 , 765-769 .
[3] Arizono, I., & Ohta, H., (1989) . A test for normality based on Kullback-Leibler information. The American Statistician, 43 , 20-22 .
[4] Balakreshnan, N., & Rad, A.H., & Arghami, N.R., (2007) . Testing exponentiality based on Kullback-Leibler information with peogressively Type-II censored data. IEEE Transactions on Reliability, 56 , 349-356 .
[5] Baratpour, S., & Khodadadi, F., (2012) . A cumulative residual entropy characterization of the Rayleigh distribution and related goodness-of-fit test. Journal of Statistical Research of Iran, 9 , 115-131 .
[6] Baratpour, S., & Rad, A.H., (2012) . Testing goodness-of fit for exponential distribution based on cumulative residual entropy. Communications in Statistics Theory and Methods, 41 , 1387-1396 .
[7] Caroni, C., (2002) . The correct ball bearing data. Lifetime Data Analysis, 8 , 395-399 .
[8] Ciumara, R., & Panait, I.I., (2018) . On Generalized Cumulative Information of Kullback-Leibler Type. Order, 2 , 1 .
[9] Di Crescenzo, A., & Longobardi, M., (2009) . On cumulative entropies. Journal of Statistical Planning and Inference, 139 , 4072-4087 .
[10] Jahanshahi, S.M.A., & Habibi Rad, A., & Fakoori, V., (2016) . A goodness of fit test Rayleigh distribution based on Hellinger distance. Annals of Data Science, 3 , 401-411 .
[11] Khorashadizadeh, M., (2018) . More results on dynamic cumulative inaccuracy measure. JIRSSJournal of The Iranian Statistical Society, 17(1) , 89-108 .
[12] Khorashadizadeh, M., & Roknabadi, A.R., & Borzadaran, G.M., (2016) . Discrete dynamic cumulative residual entropy. International Journal of Reliability and Safety, 10(3) , 210-226 .
[13] Kolmogorov, A.N., (1933) . Sulla Determinazione Empirica di une legge di Distribuzione. Giornale dell’Intituto Italiano degli Attuari, 4 , 83-91 .
[14] Kullback, S., (1959) . Information Theory and Statistics. Wiley, NY.
[15] Kuiper, N.H., (1960) . Tests concerning random points on a circle. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series A, 63 , 38-47 .
[16] Meintanis, S., & Iliopoulos, G., (2003) . Test of fit for the Rayleigh distribution based on the empirical Laplace transform. Annals of the Institute of Statistical Mathematics, 55 , 137-151 .
[17] Navarro, J., & Aguila, Y., & Asadi, M., (2010) . Some new result on the cumulative residual entropy. Journal of Statistical Planning and Inference, 140 , 310-322 .
[18] Park, S., & Noughabi, H.A., & Kim, I., (2018) . General cumulative Kullback-Leibler information. Communications in Statistics-Theory and Methods, 47(7) , 1551-1560 .
[19] Park, S., & Rao, M., & Shin, D.W., (2012) . On cumulative residual Kullback-Leibler information. Statistics and Probability Letters, 82 , 2025-2032 .
[20] Park, S., & Pakyari, R., (2015) . Cumulative residual Kullback-Leibler information with the progressively Type-II censored data. Statistics and Probability Letters, 106 , 287-294 .
[21] Rao, M., & Chen, Y., & Vemuri, B.C., & Wang, F., (2004) . Cumulative residual entropy: a new measure of information. IEEE Transactions on Information theory, 50 , 1220-1228 .
[22] Safavinejad, M., & Jomhoori, S., & Alizadeh Noughabi, H., (2015) . A devsity based empirical likelihood ratio goodness of fit test for the Rayleigh distribution and power comparison. Jornal of Statistical Computation and Simulation, 85 , 3322-3334 .
[23] Shannon, C.E., (1948) . A Mathematical of Communication. Bell System Technical Journal, 27 , 379-423 .
[24] Sunoj, S.M., & Sankaran, P.G., & Unnikrishnan Nair, N., (2018) . Quantile-based cumulative Kullback-Leibler divergence. Statistics, 52(1) , 1-17 .
[25] Watson, G.S., (1961) . Goodness of fit tests on a circle. Biometrika, 48 , 109-114 .
[26] Zohrevand, Y., & Hashemi, R., & Asadi, M., (2020) . An adjusted cumulative Kullback-Leibler information with application to test of exponentiality. Communications in Statistics-Theory and Methods, 49(1) , 44-60 .