Asymptotic inequalities and comparison of classical means

Best Possible Inequalities between Generalized Logarithmic Mean and Classical Means

and Applied Analysis 3 Theorem B. For all positive real numbers a and b with a/ b, we have √ G a, b A a, b < √ L a, b I a, b

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Inequalities and Asymptotic Estimates

Unless specified otherwise, we use µ, σ 2 to denote the mean and variance of the the variable under consideration. This note shall be updated throughout the seminar as I find more useful inequalities. 1 Basic inequalities Theorem 1.1 (Markov's Inequality). If X is a random variable taking only non-negative values, then for any a > 0 Pr[X ≥ a] ≤ E[X] a. (1) Proof. We show this for the discrete c...

a comparison of teachers and supervisors, with respect to teacher efficacy and reflection

supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...

Some Comparison Inequalities for Generalized Muirhead and Identric Means