AbstractIn this paper we study the monotonicity properties of some functions involving the Mills' ratio of the standard normal law. From these we deduce some new functional inequalities involving the Mills' ratio, and we show that the Mills' ratio is strictly completely monotonic. At the end of this paper we present some Turán-type inequalities for Mills' ratio
We prove that certain functions involving the gamma and q-gamma function are monotone. We also prove...
In this paper, by using a general result on the monotonicity of quotients of power series, our aim ...
An elementary proof of the anti-monotonicity of the quantum mechanical particle density with respec...
Consider the Mills ratio f(x) =1 − Φ(x)/φ(x), x ≥ 0, where φ is the density function of the standard...
The inverse Mills ratio is R: = φ/ Ψ , where φ and Ψ are, respectively, the probability density func...
We review various inequalities for Mills ’ ratio (1 − Φ)/φ, where φ and Φ denote the standard Gaussi...
From Springer Nature via Jisc Publications RouterHistory: received 2021-01-01, accepted 2021-10-10, ...
AbstractWe consider several properties that might be described as “monotonicity” or “absoluteness” t...
Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonic...
In the article, some strictly Logarithmically completely monotonic ratios of mean values are presen...
Koch T. Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Fun...
AbstractThis paper deals with a generalization of L’Hôspital-type rules for monotonicity. The result...
For α>0 a real number, the function x√Γ(x+1)/(x+α)√Γ(x+α+1) is increasing with x∈(x0,∞) and logarith...
AbstractIn this paper, the logarithmically complete monotonicity of the function exΓ(x+β)/xx+β−α in ...
AbstractOur main result is a list of characterizations of ∗orthant-monotonic norms
We prove that certain functions involving the gamma and q-gamma function are monotone. We also prove...
In this paper, by using a general result on the monotonicity of quotients of power series, our aim ...
An elementary proof of the anti-monotonicity of the quantum mechanical particle density with respec...
Consider the Mills ratio f(x) =1 − Φ(x)/φ(x), x ≥ 0, where φ is the density function of the standard...
The inverse Mills ratio is R: = φ/ Ψ , where φ and Ψ are, respectively, the probability density func...
We review various inequalities for Mills ’ ratio (1 − Φ)/φ, where φ and Φ denote the standard Gaussi...
From Springer Nature via Jisc Publications RouterHistory: received 2021-01-01, accepted 2021-10-10, ...
AbstractWe consider several properties that might be described as “monotonicity” or “absoluteness” t...
Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonic...
In the article, some strictly Logarithmically completely monotonic ratios of mean values are presen...
Koch T. Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Fun...
AbstractThis paper deals with a generalization of L’Hôspital-type rules for monotonicity. The result...
For α>0 a real number, the function x√Γ(x+1)/(x+α)√Γ(x+α+1) is increasing with x∈(x0,∞) and logarith...
AbstractIn this paper, the logarithmically complete monotonicity of the function exΓ(x+β)/xx+β−α in ...
AbstractOur main result is a list of characterizations of ∗orthant-monotonic norms
We prove that certain functions involving the gamma and q-gamma function are monotone. We also prove...
In this paper, by using a general result on the monotonicity of quotients of power series, our aim ...
An elementary proof of the anti-monotonicity of the quantum mechanical particle density with respec...
DOI
Add to ORKG