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Articles 50071 - 50072 of 50072
Full-Text Articles in Entire DC Network
On Characterizations Of Exponential Distribution Through Order Statistics And Record Values With Random Shifts, M. Ahsanullah, Imtiyaz A. Shah, George Yanev
On Characterizations Of Exponential Distribution Through Order Statistics And Record Values With Random Shifts, M. Ahsanullah, Imtiyaz A. Shah, George Yanev
School of Mathematical & Statistical Sciences Faculty Publications
Distributional relations of the form Y d= X +T where X, Y, and T are record values or order statistics and the random translator T is independent from X are considered. Characterizations of the exponential distribution when the ordered random variables are non-neighboring are proved. Corollaries for Pareto and power function distributions are also derived.
On Equivalent Characterizations Of Convexity Of Functions, Eleftherios Gkioulekas
On Equivalent Characterizations Of Convexity Of Functions, Eleftherios Gkioulekas
School of Mathematical & Statistical Sciences Faculty Publications
A detailed development of the theory of convex functions, not often found in complete form in most textbooks, is given. We adopt the strict secant line definition as the definitive definition of convexity. We then show that for differentiable functions, this definition becomes logically equivalent with the first derivative monotonicity definition and the tangent line definition. Consequently, for differentiable functions, all three characterizations are logically equivalent.