تعمیم هایی از اطلاع کولبک-لیبلر بر اساس تابع بقا

ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺍﺑﺘﺪﺍ ﺑﻪ ﺑﺮﺧﻲ ﺍﺯ ﺗﻌﻤﻴﻢ ﻫﺎﻱ ﺍﻃﻼﻉ ﮐﻮﻟﺒﮏ-ﻟﻴﺒﻠﺮ ﻭ ﺧﻮﺍﺹ ﺁﻥ ﻫﺎ ﭘﺮﺩﺍﺧﺘﻪ ﻣﻲ ﺷﻮﺩ. ﺳﭙﺲ ﺷﺮﺍﻳﻂ ﮔﺸﺘﺎﻭﺭﻱ ﺑﺮﺍﻱ ﺗﻮﺯﻳﻊ ﻣﺎﮐﺴﻴﻤﻢ ﺁﻧﺘﺮﻭﭘﻲ ﻣﺎﻧﺪﻩ ﻱ ﺗﺠﻤﻌﻲ ﺑﺮﺭﺳﻲ ﻭ ﺭﺍﺑﻄﻪ ﻱ ﺑﻴﻦ ﺍﻃﻼﻉ ﮐﻮﻟﺒﮏ-ﻟﻴﺒﻠﺮ ﻣﺎﻧﺪﻩ ﻱ ﺗﺠﻤﻌﻲ (crkl) ﻭ ﺁﻧﺘﺮﻭﭘﻲ ﻣﺎﻧﺪﻩ ﻱ ﺗﺠﻤﻌﻲ (cre) ﻣﻄﺎﻟﻌﻪ ﻣﻲ ﺷﻮﺩ. ﻫﻤﭽﻨﻴﻦ ﺩﺭ ﻣﻮﺭﺩ ﺭﻭﺵ ﻫﺎﻱ ﺑﺮﺁﻭﺭﺩ ﭘﺎﺭﺍﻣﺘﺮ ﻣﻘﻴﺎﺱ ﺗﻮﺯﻳﻊ ﺭﺍﻳﻠﻲ ﺑﺤﺚ ﺷﺪﻩ ﻭ ﺩﻭ ﺭﻭﺵ ﺑﺮﺁﻭﺭﺩ ﺁﻥ ﺍﺭﺍﺋﻪ ﻣﻲ ﺷﻮﺩ. ﺩﺭ ﺍﺩﺍﻣﻪ ﺍﻃﻼﻉ ﮐﻮﻟﺒﮏ-ﻟﻴﺒﻠﺮ ﻣﺎﻧﺪﻩ ﻱ ﺗﺠﻤﻌﻲ ﺭﺍ ﺑﻪ ﻋﻨﻮﺍﻥ ﻳﮏ ﺁﻣﺎﺭﻩ ﺁﺯﻣﻮﻥ ﻧﻴﮑﻮﻳﻲ ﺑﺮﺍﺯﺵ ﺑﻪ ﮐﺎﺭ ﺑﺮﺩﻩ ﻭ ﺳﭙﺲ ﻣﻘﺎﺩﻳﺮ ﺑﺤﺮﺍﻧﻲ ﻭ ﺗﻮﺍﻥ ﺁﺯﻣﻮﻥ ﻫﺎﻱ ﭘﻴﺸﻨﻬﺎﺩﻱ ﻣﺤﺎﺳﺒﻪ ﻭ ﺑﺎ ﺗﻮﺍﻥ ﺳﺎﻳﺮ ﺁﺯﻣﻮﻥ ﻫﺎ ﻣﻘﺎﻳﺴﻪ ﻣﻲ ﺷﻮﺩ. ﺩﺭ ﭘﺎﻳﺎﻥ، ﺁﺯﻣﻮﻥ ﻫﺎ ﺑﺮﺍﻱ ﻳﮏ ﻣﺠﻤﻮﻋﻪ ﺩﺍﺩﻩ ﻱ ﻭﺍﻗﻌﻲ ﺑﻪ ﮐﺎﺭ ﮔﺮﻓﺘﻪ ﻣﻲ ﺷﻮﺩ

Some extensions of Kullback-Leibler information based on survival function

In this article, we first investigate some extensions of KullbackLeibler information and theirproperties. Then, we consider the moment constraints for the maximum distribution of cumulative residualentropy and investigate the relationship between the cumulative residual KullbackLeibler information(CRKL) and cumulative residual entropy (CRE). We also discuss the methods for estimating the scaleparameter of Rayleigh distribution and provide two estimation methods. In the following we use cumulativeresidual KullbackLeibler information as a goodness of fit test statistic. Then we compute the criticalvalues 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.