آﻧﺘﺮوﭘﯽ ﻣﺎﻧﺪه ﺗﺴﺎﻟﯿﺲ و اﻧﺪازه واﮔﺮاﯾﯽ آن ﻣﺒﺘﻨﯽ ﺑﺮ ﺗﺎﺑﻊ ﭼﻨﺪك

Quantile Based Tsallis Residual Entropy and its Divergence Measure

ﭼﮑﯿﺪه: آﻧﺘﺮوﭘﯽ ﻧﻘﺶ اﺳﺎﺳﯽ در ﻣﺒﺎﺣﺚ ﻗﺎﺑﻠﯿﺖ اﻋﺘﻤﺎد و ﻣﻄﺎﻟﻌﺎت ﻃﻮل ﻋﻤﺮ ﺳﯿﺴﺘﻢ ﻫﺎ اﯾﻔﺎ ﻣﯽ ﮐﻨﺪ. در ﻣﻄﺎﻟﻌﺎت اﺧﯿﺮ ﺗﻮﺟﻪ زﯾﺎدي ﺑﻪ اﺳﺘﻔﺎده از ﺗﺎﺑﻊ ﭼﻨﺪك، ﺧﻮاص و ﮐﺎرﺑﺮدﻫﺎي آن ﺑﻪ ﻋﻨﻮان روﯾﮑﺮدي ﺟﺎﯾﮕﺰﯾﻦ در ﺗﺸﺨﯿﺺ ﻣﺪل ﻫﺎي آﻣﺎري و ﺗﺤﻠﯿﻞ داده ﻫﺎ ﺷﺪه اﺳﺖ. در ﻣﻘﺎﻟﻪ ﺣﺎﺿﺮ آﻧﺘﺮوﭘﯽ ﻣﺎﻧﺪه ﺗﺴﺎﻟﯿﺲ ﻣﺒﺘﻨﯽ ﺑﺮ ﺗﺎﺑﻊ ﭼﻨﺪك ﻣﻌﺮﻓﯽ و ﺑﻪ ﺑﺮرﺳﯽ ﺧﻮاص آن در ﻣﺪل ﻫﺎي ﭘﯿﻮﺳﺘﻪ ﭘﺮداﺧﺘﻪ ﻣﯽ ﺷﻮد. ﺑﺎ در ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﺗﻮزﯾﻊ ﻫﺎي ﻃﻮل ﻋﻤﺮ ﺧﺎص، ﺻﻮرت ﻫﺎﯾﯽ ﺑﺴﺘﻪ ﺑﺮاي آﻧﺘﺮوﭘﯽ ﻣﺎﻧﺪه ﺗﺴﺎﻟﯿﺲ ﭼﻨﺪﮐﯽ ﺑﻪ دﺳﺖ آورده و ﺧﻮاص ﯾﮑﻨﻮاﯾﯽ آﻧﻬﺎ را ﻣﻮرد ﻣﻄﺎﻟﻌﻪ ﻗﺮار داده و ﺑﻪ ﻣﺸﺨﺺ ﺳﺎزي ﺑﺮ اﺳﺎس اﯾﻦ آﻧﺘﺮوﭘﯽ ﭘﺮداﺧﺘﻪ ﺷﺪه اﺳﺖ. ﻫﻤﭽﻨﯿﻦ اﻧﺪازه واﮔﺮاﯾﯽ ﺗﺴﺎﻟﯿﺲ ﺑﺮ ﻣﺒﻨﺎي ﺗﺎﺑﻊ ﭼﻨﺪك و ﺷﮑﻞ ﭼﻨﺪﮐﯽ آن ﺑﺮاي ﻣﺘﻐﯿﺮ ﻣﺎﻧﺪه ﻋﻤﺮ ﺑﻪ دﺳﺖ آورده ﻣﯽ ﺷﻮد. در ﻧﻬﺎﯾﺖ ﯾﮏ ﺑﺮآوردﮔﺮ ﺑﺮاي آﻧﺘﺮوﭘﯽ ﻣﺎﻧﺪه ﺗﺴﺎﻟﯿﺲ ﭼﻨﺪﮐﯽ ﻣﻌﺮﻓﯽ ﺷﺪه و ﺑﺎ ﻣﻄﺎﻟﻌﻪ ﺷﺒﯿﻪ ﺳﺎزي، ﻋﻤﻠﮑﺮد آن ﻣﻮرد ﺑﺮرﺳﯽ ﻗﺮار ﮔﺮﻓﺘﻪ اﺳﺖ.

Entropy plays a fundamental role in reliability and system lifetesting areas. In the recent studies, much attentions have been paid to use quantile functions properties and their applications as an alternate approac in distinguishing statistical models and analysis of data. In the present paper, quantile based residual Tsallis entropy is introduced and its properties in continuous models are investigated. Considering distributions of certain lifetime, explicit versions for quantile based residual Tsallis entropy are obtained and their properties monotonicity are studied and characterization based on this entropy is investigated. Also quantile based Tsallis divergence is introduced and quantile based residual Tsallis divergence is obtained. Finally, an estimator for the quantile based residual Tsallis entropy is introduced and its performance is investigate by study simulation.