ﺑﺮآورد ﭘﺎراﻣﺘﺮﻫﺎي ﻣﮑﺎن و ﺷﮑﻞ ﺗﻮزﯾﻊ ﮔﻮﻣﭙﺮﺗﺰ ﺑﺎ آﻣﺎره ﻫﺎي ﺗﺮﺗﯿﺒﯽ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ

Estimation of Location and Shape Parameters for the Gompertz Distribution Using Generalized Order Statistics

ﭼﮑﯿﺪه: در اﯾﻦ ﻣﻘﺎﻟﻪ ﺿﻤﻦ اراﺋﻪ روش ﺗﻮﻟﯿﺪ آﻣﺎره ﻫﺎي ﺗﺮﺗﯿﺒﯽ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ از ﺗﻮزﯾﻊ ﮔﻮﻣﭙﺮﺗﺰ، ﺑﺮآوردﻫﺎي ﺑﯿﺰي و ﻣﺎﮐﺴﯿﻤﻢ درﺳﺘﻨﻤﺎﯾﯽ ﭘﺎراﻣﺘﺮﻫﺎ و ﺗﺎﺑﻊ ﻫﺎي ﻗﺎﺑﻠﯿﺖ اﻋﺘﻤﺎد و ﺧﻄﺮ آن در ﻃﺮح ﻫﺎي ﺳﺎﻧﺴﻮر ﺷﺪه ﻓﺰآﯾﻨﺪه ﻧﻮع دوم و ﻣﻘﺎدﯾﺮ رﮐﻮردﻫﺎ ﺑﺮ اﺳﺎس آﻣﺎره ﻫﺎي ﺗﺮﺗﯿﺒﯽ ﺑﻪ دﺳﺖ آورده ﺷﺪه و ﺑﺎ اﺳﺘﻔﺎده از ﺷﺒﯿﻪ ﺳﺎزي ﻣﻮﻧﺖ ﮐﺎرﻟﻮ و دو ﻣﺠﻤﻮﻋﻪ داده واﻗﻌﯽ ﻣﻘﺎﯾﺴﻪ ﻣﯽ ﺷﻮﻧﺪ. ﻫﻤﭽﻨﯿﻦ ﺑﺎ ﻣﻘﺎﯾﺴﻪ ﺑﺮآوردﻫﺎي ﺑﯿﺰي و ﻣﺎﮐﺴﯿﻤﻢ درﺳﺘﻨﻤﺎﯾﯽ ﺗﻮزﯾﻊ ﮔﻮﻣﭙﺮﺗﺰ ﺑﺎ ﺑﺮآوردﻫﺎي ﻣﺸﺎﺑﻪ در ﺗﻮزﯾﻊ ﻫﺎي واﯾﺒﻮل و ﻟﻮﻣﺎﮐﺲ ﻧﺸﺎن داده ﻣﯽ ﺷﻮد ﮐﻪ ﺑﺮآوردﻫﺎي ﺗﻮزﯾﻊ ﮔﻮﻣﭙﺮﺗﺰ ﺑﻬﺘﺮﻧﺪ.

In this paper, based on generalized order statistics the Bayesian and maximum liklihood estimations of the parameters, the reliability and the hazard functions of Gompertz distribution are investigated. Specializations to Bayesian and maximum liklihood estimators, some lifetime parameters of progressive II censoring and record values are obtained. Also by using two real data sets and simulated data accurations of different estimates of the parameters are compared. Next the Bayesian and maximum liklihood estimates of the Gompertz distribution are compared with Weibull and Lomax distrtibutions.