آزمون-برآورديابي انقباضي در توزيع رايلي و كاربرد آن در داده هاي سانسور شده نوع دوم

Shrinkage Testimation in Rayleigh Distribution and it's Application in Type-II Censored Data

ﻓﺮض ﮐﻨﯿﺪ ﯾﮏ ﻧﻤﻮﻧﻪ ﺗﺼﺎدﻓﯽ از ﺗﻮزﯾﻊ راﯾﻠﯽ ﺗﮏ ﭘﺎراﻣﺘﺮي در اﺧﺘﯿﺎر ﺑﺎﺷﺪ. در روش ﻫﺎي ﮐﻼﺳﯿﮏ آﻣﺎر، ﺑﺮاﺳﺎس اﻃﻼﻋﺎت ﻣﻮﺟﻮد در ﻧﻤﻮﻧﻪ و ﺑﺎ روش ﻫﺎي ﻣﻌﻤﻮل ﺑﻪ ﺑﺮآوردﯾﺎﺑﯽ ﭘﺎراﻣﺘﺮ ﻧﺎﻣﻌﻠﻮم ﭘﺮداﺧﺘﻪ ﻣﯽ ﺷﻮد. ﮔﺎﻫﯽ در ﻋﻤﻞ، ﻣﺤﻘﻖ داراي اﻃﻼﻋﺎﺗﯽ درﺑﺎره ﭘﺎراﻣﺘﺮ ﻧﺎﻣﻌﻠﻮم ﺑﻪ ﺻﻮرت ﯾﮏ ﺣﺪس ﯾﺎ ﮔﻤﺎن ﻣﯽ ﺑﺎﺷﺪ. اﯾﻦ ﺣﺪس، اﻃﻼﻋﺎت ﻏﯿﺮﻧﻤﻮﻧﻪ اي ﻧﺎﻣﯿﺪه ﻣﯽ ﺷﻮد. در اﯾﻦ ﺣﺎﻟﺖ، ﺑﺮآوردﮔﺮﻫﺎي اﻧﻘﺒﺎﺿﯽ ﺧﻄﯽ ﺑﺎ ﺗﺮﮐﯿﺐ اﻃﻼﻋﺎت ﻏﯿﺮﻧﻤﻮﻧﻪ اي و اﻃﻼﻋﺎت ﻣﻮﺟﻮد در ﻧﻤﻮﻧﻪ ﻣﻌﺮﻓﯽ ﺷﺪﻧﺪ ﮐﻪ در ﻧﺰدﯾﮑﯽ ﻣﻘﺪار ﺣﺪﺳﯽ و واﻗﻌﯽ داراي ﻣﺨﺎﻃﺮه ﮐﻤﺘﺮي ﻧﺴﺒﺖ ﺑﻪ ﺑﺮآوردﮔﺮﻫﺎي ﻣﻌﻤﻮل ﻫﺴﺘﻨﺪ. در اﯾﻦ ﻣﻘﺎﻟﻪ، ﺑﺮاﺳﺎس رد ﯾﺎ ﭘﺬﯾﺮش ﻓﺮﺿﯿﻪ ﺻﻔﺮ ﻧﺰدﯾﮑﯽ ﻣﻘﺪار ﺣﺪﺳﯽ و ﻣﻘﺪار واﻗﻌﯽ ﭘﺎراﻣﺘﺮ، ﭼﻨﺪ آزﻣﻮن-ﺑﺮآوردﮔﺮ اﻧﻘﺒﺎﺿﯽ ﺑﺮاي ﭘﺎراﻣﺘﺮ ﻣﻮرد ﺑﺮرﺳﯽ ﺑﺎ روش ﻫﺎي ﻣﺨﺘﻠﻒ، ﻣﻌﺮﻓﯽ و ﻣﺨﺎﻃﺮه آن ﻫﺎ ﺗﺤﺖ ﺗﺎﺑﻊ زﯾﺎن آﻧﺘﺮوﭘﯽ ﻣﺤﺎﺳﺒﻪ ﻣﯽ ﺷﻮد. ﺳﭙﺲ رﻓﺘﺎر آزﻣﻮن-ﺑﺮآوردﮔﺮﻫﺎي اﻧﻘﺒﺎﺿﯽ و ﺑﻬﺘﺮﯾﻦ ﺑﺮآوردﮔﺮ ﺧﻄﯽ ﺑﺮاﺳﺎس ﮐﺎراﯾﯽ ﻧﺴﺒﯽ ﺑﯿﻦ آن ﻫﺎ ﻣﻘﺎﯾﺴﻪ ﻣﯽ ﺷﻮﻧﺪ. آن ﮔﺎه ﻧﺘﺎﯾﺞ ﺑﻪ دﺳﺖ آﻣﺪه ﺑﺮاي ﻧﻤﻮﻧﻪ ﻫﺎي ﺳﺎﻧﺴﻮر ﺷﺪه ﻧﻮع دوم ﺑﻪ ﮐﺎر ﮔﺮﻓﺘﻪ ﻣﯽ ﺷﻮد.

Suppose that we have a random sample from one-parameter Rayleigh distribution. In classical methods, we estimate the interesting parameter based on the sample information and with usual estimators. Sometimes in practice, the researcher has some information about the unknown parameter in the form of a guess value. This guess is known as nonsample information. In this case, linear shrinkage estimators are introduced by combining nonsample and sample information which have smaller risk than usual estimators in the vicinity of guess and true value. In this paper, some shrinkage testimators are introduced using different methods based on vicinity of guess value and true parameter and their risks are computed under the entropy loss function. Then, the performance of shrinkage testimators and the best linear estimator is calculated via the relative efficiency of them. Therefore, the results are applied for the type-II censored data.