توزيع مقادير كرانگين موزون و ويژگي هاي آن

The Weighted Extreme Value Distributions and Its Properties

ﭼﮑﯿﺪه: در اﯾﻦ ﻣﻘﺎﻟﻪ ﯾﮏ ﺗﻮزﯾﻊ وزن دار ﺷﺪه ﺟﺪﯾﺪ ﺑﺮ ﭘﺎﯾﻪ ﺗﻮزﯾﻊ ﻣﻘﺎدﯾﺮ ﮐﺮاﻧﮕﯿﻦ ﻣﻌﺮﻓﯽ ﻣﯽ ﮔﺮدد. وﯾﮋﮔﯽ ﻫﺎ و ﻣﺸﺨﺼﻪ ﻫﺎي اﺳﺎﺳﯽ اﯾﻦ ﺗﻮزﯾﻊ از ﻗﺒﯿﻞ ﺗﺎﺑﻊ ﺗﻮزﯾﻊ ﺗﺠﻤﻌﯽ، ﺗﺎﺑﻊ ﻣﻮﻟﺪ ﮔﺸﺘﺎور، ﺿﺮﯾﺐ ﭼﻮﻟﮕﯽ و ﮐﺸﯿﺪﮔﯽ ﻣﻮرد ﺑﺮرﺳﯽ ﻗﺮار ﻣﯽ ﮔﯿﺮد. ﭘﺲ از ﺑﻪ دﺳﺖ آوردن ﺑﺮآوردﮔﺮﻫﺎي ﻣﺎﮐﺴﯿﻤﻢ درﺳﺘﻨﻤﺎﯾﯽ ﭘﺎراﻣﺘﺮﻫﺎ، دو ﻣﺜﺎل واﻗﻌﯽ ﺑﺮاي ﺑﺮرﺳﯽ ﻣﻨﺎﺳﺐ ﺑﻮدن ﻣﺪل و ﻋﻤﻠﮑﺮد ﺑﺮآوردﮔﺮﻫﺎ اراﺋﻪ ﺷﺪه اﺳﺖ.

This paper introduces a new distribution based on extreme value distribution. Some properties and characteristics of the new distribution such as distribution function, moment generating function and skewness and kurtosis are studied. Finally, by computing the maximum likelihood estimators of the new distribution's parameters, the performance of the model is illustrated via two real examples.