اﺳﺘﻨﺒﺎط ﺑﺮاي ﺗﻮزﯾﻊ ﻧﻤﺎﯾﯽ ﻣﻌﮑﻮس ﺗﻌﻤﯿﻢﯾﺎﻓﺘﻪ ﺑﺮاﺳﺎس دادهﻫﺎي ﺳﺎﻧﺴﻮر ﻫﯿﺒﺮﯾﺪ ﻓﺰاﯾﻨﺪه ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ و ﮐﺎرﺑﺮد آن در دادهﻫﺎي ﭘﺎﺷﺶ ﭘﻼﺳﻤﺎﯾﯽ

Inference for generalized inverse exponential distribution based on generalized hybrid Progressive censored data and its application to plasma spray data

در ﺑﺴﯿﺎري از ﺗﺤﻘﯿﻘﺎت ﮐﺎرﺑﺮدي ﺑﻪ دﻻﯾﻠﯽ ﻫﻤﭽﻮن ﻣﺤﺪودﯾﺖ زﻣﺎﻧﯽ و ﻣﺎﻟﯽ، ﭘﮋوﻫﺸﮕﺮ ﺑﻪ ﺗﻤﺎﻣﯽ دادهﻫﺎ دﺳﺘﺮﺳﯽ ﻧﺪارد. ﺑﻨﺎﺑﺮاﯾﻦ اﺳﺘﻨﺒﺎط آﻣﺎري ﺑﺮاﺳﺎس اﻃﻼﻋﺎت واﺣﺪﻫﺎﯾﯽ از ﻧﻤﻮﻧﻪ ﮐﻪ در دﺳﺘﺮس ﻣﯽﺑﺎﺷﻨﺪ، ﺣﺎﺋﺰ اﻫﻤﯿﺖ اﺳﺖ. در اﯾﻦ ﻣﻘﺎﻟﻪ، روشﻫﺎي ﻣﺨﺘﻠﻒ ﺑﺮآورد ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺠﻬﻮل ﺗﻮزﯾﻊ ﻧﻤﺎﯾﯽ ﻣﻌﮑﻮس ﺗﻌﻤﯿﻢﯾﺎﻓﺘﻪ ﺗﺤﺖ دادهﻫﺎي ﺳﺎﻧﺴﻮرﺷﺪه ي ﻫﯿﺒﺮﯾﺪ ﻓﺰاﯾﻨﺪه ﺗﻌﻤﯿﻢﯾﺎﻓﺘﻪ ﻧﻮع دوم، ﻣﻄﺎﻟﻌﻪ ﺷﺪه اﺳﺖ. ﺑﺮآوردﮔﺮ ﻣﺎﮐﺴﯿﻤﻢ درﺳﺘﻨﻤﺎﯾﯽ ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺠﻬﻮل ﺗﻮزﯾﻊ و وﺟﻮد و ﯾﮑﺘﺎﯾﯽ آنﻫﺎ ﺑﺮرﺳﯽ ﮔﺮدﯾﺪه اﺳﺖ. ﺑﺮاﺳﺎس دﯾﺪﮔﺎه ﺑﯿﺰي، ﺑﺮآورد ﭘﺎراﻣﺘﺮﻫﺎي ﺷﮑﻞ و ﻣﻘﯿﺎس ﺗﻮزﯾﻊ ﺑﺎ اﺳﺘﻔﺎده از ﺗﺎﺑﻊ زﯾﺎن ﻣﺮﺑﻊ ﺧﻄﺎ ﻣﺤﺎﺳﺒﻪ ﺷﺪه اﺳﺖ. از آﻧﺠﺎ ﮐﻪ ﺑﺮآوردﮔﺮ ﺑﯿﺰي ﭘﺎراﻣﺘﺮﻫﺎ ﻓﺮم ﺑﺴﺘﻪاي ﻧﺪارﻧﺪ، ﺗﻘﺮﯾﺐﻫﺎي ﻟﯿﻨﺪﻟﯽ و ﻧﻤﻮﻧﻪ ﮔﯿﺮي از ﻧﻘﺎط ﻣﻬﻢ، ﺑﺮاي ﻣﺤﺎﺳﺒﻪ ﺑﺮآوردﮔﺮﻫﺎ اﺳﺘﻔﺎده ﺷﺪه اﺳﺖ. ﻣﻄﺎﻟﻌﻪ ﺷﺒﯿﻪﺳﺎزي ﺑﺮاي ﻣﻘﺎﯾﺴﻪ ﺑﺮآوردﮔﺮﻫﺎي ﻣﺨﺘﻠﻒ ﮐﻼﺳﯿﮏ و ﺑﯿﺰي، اراﺋﻪ ﮔﺮدﯾﺪه اﺳﺖ. در ﭘﺎﯾﺎن، دو ﻣﺜﺎل واﻗﻌﯽ ﺷﺎﻣﻞ دادهﻫﺎي ﻣﺮﺑﻮط ﺑﻪ ﺑﺮﺧﻮرد ﻣﺎﯾﻞ ﻣﯿﮑﺮو ﻗﻄﺮه در ﻓﺮآﯾﻨﺪ ﭘﺎﺷﺶ ﭘﻼﺳﻤﺎﯾﯽ و زﻣﺎن ﺗﻌﻤﯿﺮ ﻣﺮﺑﻮط ﺑﻪ ﯾﮏ ﻓﺮﺳﺘﻨﺪه ارﺗﺒﺎﻃﯽ، ﺑﺮاي ﻧﺸﺎن دادن ﺑﻬﺘﺮ اﻫﺪاف ﻣﻘﺎﻟﻪ، اراﺋﻪ ﮔﺮدﯾﺪه اﺳﺖ.

In many applied research, the researcher does not have access to all the data for some reasons such as time and cost constraints. So, the statistical inference based on the available data is important. In this paper, estimation of unknown parameters of a generalized inverted exponential distribution is studied under generalized Type II progressive hybrid censoring. The maximum likelihood estimators and their existence and uniqueness are investigated. Based on the Bayesian approach, the estimators of the shape and scale parameters are derived under squared error loss function. Since closed - form expressions for the Bayes estimators cannot be obtained, we use Lindley’s approximation and important sampling procedure for obtaining them. Simulation study for comparing the different classical and Bayesian estimations is presented. Finally, two real data sets contain oblique impact of micro droplets onto surface in plasma spray coating process and repair time for a communication transmitter are analyzed for illustration purposes.