18,469 research outputs found
Some Properties of the Generalized Stuttering Poisson Distribution and Its Applications
Based on the probability generating function of stuttering Poisson distribution (SPD), this paper considers some equivalent propositions of SPD. From this, we show that some distributions in the application of non-life insurance actuarial science are SPD, such as negative binomial distribution, compound Poisson distribution etc.. By weakening condition of equivalent propositions of SPD, we define the generalized SPD and prove that any non-negative discrete random variable X with P{X = 0} > 0.5 obey generalized SPD. Then, we discuss the waiting time distribution of generalized stuttering Poisson process. We consider cumulant estimation of generalized SPD's parameters. As an application, we use SPD with four parameters (4th SPD) to fit auto insurance claim data. The fitting results show that 4th SPD is more accurate than negative binomial and Poisson distribution
Bounding the convex combination of arithmetic and integral means in terms of one-parameter harmonic and geometric means
The Schur concavity, Schur multiplicative and harmonic convexities of the second dual form of the Hamy symmetric function with applications
AbstractFor x=(x1,x2,…,xn)∈R+n, the second dual form of the Hamy symmetric function is defined by Hn∗∗(x,r)=Hn∗∗(x1,x2,…,xn;r)=∏1≤i1<i2<⋯<ir≤n(∑j=1rxij)1r, where r∈{1,2,…,n} and i1,i2,…,in are positive integers.In this paper, we prove that Hn∗∗(x,r) is Schur concave, and Schur multiplicatively and harmonic convex in R+n. Some applications in inequalities and reliability theory are presented
Sharp One-Parameter Mean Bounds for Yang Mean
We prove that the double inequality Jα(a,b)<U(a,b)<Jβ(a,b) holds for all a,b>0 with a≠b if and only if α≤2/(π-2)=0.8187⋯ and β≥3/2, where U(a,b)=(a-b)/[2arctan((a-b)/2ab)], and Jp(a,b)=p(ap+1-bp+1)/[(p+1)(ap-bp)] (p≠0,-1), J0(a,b)=(a-b)/(loga-logb), and J-1(a,b)=ab(loga-logb)/(a-b) are the Yang and pth one-parameter means of a and b, respectively
Engineering artificial atomic systems of giant electric dipole moment
The electric dipole moment (EDM) plays a crucial role in determining the
interaction strength of an atom with electric fields, making it paramount to
quantum technologies based on coherent atomic control. We propose a scheme for
engineering the potential in a Paul trap to realize a two-level quantum system
with a giant EDM formed by the motional states of a trapped electron. We show
that, under realistic experimental conditions, the EDM can significantly exceed
the ones attainable with Rydberg atoms. Furthermore, we show that such
artificial atomic dipoles can be efficiently initialized, readout, and
coherently controlled, thereby providing a potential platform for quantum
technologies such as ultrahigh-sensitivity electric-field sensing.Comment: 7 pages, 4 5 figures + 26 pages Supplemental Material. Comments are
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