تحلیل نابرابری های اقتصادی با استفاده از تبدیل زمان کل آزمون دومتغیره و تابع مفصل

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار گروه آمار، دانشکده علوم پایه، دانشگاه ولایت ایرانشهر، ایران

2 استاد گروه آمار، دانشکده علوم ریاضی، دانشگاه فردوسی مشهد، ایران

10.22075/jem.2025.36678.1986

چکیده

در این پژوهش، به بررسی ارتباط بین دو شاخص مهم اقتصادی یعنی درآمد و ثروت پرداخته شده است. با وجود شباهت‌های ظاهری در رفتار این دو متغیر، موارد متعددی وجود دارد که نشان‌دهنده تفاوت‌ها و عدم همبستگی کامل بین آنهاست. هدف اصلی مقاله، تحلیل ساختار وابستگی بین درآمد و ثروت افراد جامعه با بهره‌گیری از ابزارهای آماری پیشرفته است. برای مدل‌سازی وابستگی بین درآمد و ثروت، از تابع مفصل به عنوان یکی از ابزارهای نوین در نظریه احتمال استفاده شده است. در این راستا، ابتدا توابع مفصل مختلف مورد بررسی قرار گرفته و دو خانواده‌ی مفصل کلیتون و خانواده مفصل­های فورلی-گامبل-مورگنستن  (FGM)به عنوان مناسب‌ترین گزینه‌ها برای داده‌های مورد مطالعه شناسایی شده اند. همچنین، در ادامه پژوهش یک شاخص دو متغیره جدید بر پایه‌ی تبدیل زمان کل آزمون (TTT) در حالت دومتغیره و با استفاده از توابع مفصل معرفی گردیده است. این شاخص بر روی داده‌های واقعی مربوط به درآمد و ثروت خانوارهای ایرانی اعمال و نتایج حاصل، ارتباط معنا‌داری را بین این دو متغیر در سطح جامعه نشان می دهد. بنابراین می توان نتیجه گرفت که استفاده از این شاخص در داده های اقتصادی نشان می دهد که شاخص پیشنهادی زمان کل آزمون دومتغیره می تواند ساختار وابستگی بین داده‌های درآمد و ثروت را به‌صورت مؤثری نمایش دهد.  همچنین استفاده از توابع مفصل کلیتون و FGM نیز تطابق مناسب با داده‌های تجربی را نشان می دهد.

کلیدواژه‌ها


عنوان مقاله [English]

Analysis of economic inequalities using bivariate total time on test transform and copula function

نویسندگان [English]

  • Mojtaba Esfahani 1
  • Gholam Reza Mohtashami Borzadaran 2
  • Mohammad Amini 2
1 Assistant Professor in statistics, Department of Statistics, Velayat University of Iranshahr
2 Professor in Statistics, Department of Statistics, Ferdowsi University of Mashhad
چکیده [English]

This study investigates the relationship between two key economic indicators: income and wealth. Despite apparent similarities in the behavior of these two variables, numerous instances highlight their differences and lack of complete correlation. The main objective of this paper is to analyze the dependency structure between individuals’ income and wealth using advanced statistical tools. To model the dependency between income and wealth, the copula function—an innovative tool in probability theory—has been employed. In this regard, various copula functions are examined, and the Clayton copula family along with the Farlie-Gumbel-Morgenstern (FGM) copula family are identified as the most suitable choices for the studied data. Additionally, the study introduces a new bivariate index based on the Total Time on Test (TTT) transform in the bivariate case, utilizing copula functions. This index is applied to real-world data on the income and wealth of Iranian households, and the results demonstrate a significant relationship between the two variables at the societal level. Therefore, it can be concluded that using this index in economic data reveals that the proposed bivariate TTT index can effectively represent the dependency structure between income and wealth. Furthermore, the use of Clayton and FGM copulas also shows a good fit with the empirical data.

کلیدواژه‌ها [English]

  • Bivariate total time on test transform
  • Income inequality
  • Copula function
  • TTT Plot
  • Lorenz curve
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