Assuming that CX,Y is the copula function of X and Y with marginal distribution functions FX(x) and FY(y) , in this work we study the selection distribution Z=d(X|Y∈T) . We present some special cases of our proposed distribution, among them, skew-normal distribution as well as normal distribution. Some properties such as moments and moment generating function are investigated. Also, some numerical analysis is presented for illustration.
We study oscillatory properties of solutions of the Emden-Fowler type differential equation $$u^{(n)}(t)+p(t)\big |u(\sigma (t))\big |^\lambda \operatorname{sign} u(\sigma (t))=0,$$ where $0<\lambda <1$, $p\in L_{\rm loc }(\Bbb R_+;\Bbb R)$, $\sigma \in C(\Bbb R_+;\Bbb R_+)$ and $\sigma (t)\ge t$ for $t\in \Bbb R_+$. \endgraf Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established. \endgraf Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998).
For the equation y (n) + |y| k sgn y = 0, k > 1, n = 3, 4, existence of oscillatory solutions y = (x ∗ − x) −α h(log(x ∗ − x)), α = n ⁄ k − 1 , x < x∗ , is proved, where x ∗ is an arbitrary point and h is a periodic non-constant function on R. The result on existence of such solutions with a positive periodic non-constant function h on R is formulated for the equation y (n) = |y| k sgn y, k > 1, n = 12, 13, 14.
Geometric random sums arise in various applied problems like physics, biology, economics, risk processes, stochastic finance, queuing theory, reliability models, regenerative models, etc. Their asymptotic behaviors with convergence rates become a big subject of interest. The main purpose of this paper is to study the asymptotic behaviors of normalized geometric random sums of independent and identically distributed random variables via Gnedenko's Transfer Theorem. Moreover, using the Zolotarev probability metric, the rates of convergence in some weak limit theorems for geometric random sums are estimated.
The asymptotic behaviour of universal fuzzy measures is investigated in the present paper. For each universal fuzzy measure a class of fuzzy measures preserving some natural properties is defined by means of convergence with respect to ultrafilters.
The paper describes asymptotic properties of a strongly nonlinear system $\dot{x}=f(t,x)$, $(t,x)\in \mathbb{R}\times \mathbb{R}^n$. The existence of an $\lfloor {}n/2\rfloor$ parametric family of solutions tending to zero is proved. Conditions posed on the system try to be independent of its linear approximation.
The (modified) two-parametric Mittag-Leffler function plays an essential role in solving the so-called fractional differential equations. Its asymptotics is known (at least for a subset of its domain and special choices of the parameters). The aim of the paper is to introduce a discrete analogue of this function as a solution of a certain two-term linear fractional difference equation (involving both the Riemann-Liouville as well as the Caputo fractional h-difference operators) and describe its asymptotics. Here, we shall employ our recent results on stability and asymptotics of solutions to the mentioned equation.
The paper gives some basic ideas of both the construction and investigation of the properties of the Bayesian estimates of certain parametric functions of the parent exponential distribution under the model of random censorship assuming the Koziol-Green model. Various prior distributions are investigated and the corresponding estimates are derived. The stress is put on the asymptotic properties of the estimates with the particular stress on the Bayesian risk. Small sample properties are studied via simulations in the special case.